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Kombinatorika - Wikipedia bahasa Indonesia, ensiklopedia bebas
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height: 1.125em;"> <img class="mw-logo-tagline" alt="Ensiklopedia Bebas" src="/static/images/mobile/copyright/wikipedia-tagline-id.svg" width="120" height="14" style="width: 7.5em; height: 0.875em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Istimewa:Pencarian" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Cari di Wikipedia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Pencarian</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Telusuri Wikipedia" aria-label="Telusuri Wikipedia" autocapitalize="sentences" title="Cari di Wikipedia [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Istimewa:Pencarian"> </div> <button class="cdx-button cdx-search-input__end-button">Cari</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Perkakas pribadi"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Tampilan"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Tampilan" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Tampilan</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_id.wikipedia.org&uselang=id" class=""><span>Menyumbang</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Istimewa:Buat_akun&returnto=Kombinatorika" title="Anda dianjurkan untuk membuat akun dan masuk log; meskipun, hal itu tidak diwajibkan" class=""><span>Buat akun baru</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Istimewa:Masuk_log&returnto=Kombinatorika" title="Anda disarankan untuk masuk log, meskipun hal itu tidak diwajibkan. 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[o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Masuk log</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Halaman penyunting yang telah keluar log <a href="/wiki/Bantuan:Pengantar" aria-label="Pelajari lebih lanjut tentang menyunting"><span>pelajari lebih lanjut</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Istimewa:Kontribusi_saya" title="Daftar suntingan yang dibuat dari alamat IP ini [y]" accesskey="y"><span>Kontribusi</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Istimewa:Pembicaraan_saya" title="Pembicaraan tentang suntingan dari alamat IP ini [n]" accesskey="n"><span>Pembicaraan</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"><!-- CentralNotice --></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Situs"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Daftar isi" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Daftar isi</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">pindah ke bilah sisi</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">sembunyikan</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Awal</div> </a> </li> <li id="toc-Referensi" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Referensi"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Referensi</span> </div> </a> <ul id="toc-Referensi-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Daftar isi" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Gulingkan daftar isi" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Gulingkan daftar isi</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Kombinatorika</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Pergi ke artikel dalam bahasa lain. Terdapat 79 bahasa" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-79" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">79 bahasa</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%88%A5%E1%8A%90_%E1%8C%A5%E1%88%9D%E1%88%A8%E1%89%B5" title="ሥነ ጥምረት – Amharik" lang="am" hreflang="am" data-title="ሥነ ጥምረት" data-language-autonym="አማርኛ" data-language-local-name="Amharik" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AA%D8%AD%D9%84%D9%8A%D9%84_%D8%AA%D9%88%D8%A7%D9%81%D9%8A%D9%82%D9%8A" title="تحليل توافيقي – Arab" lang="ar" hreflang="ar" data-title="تحليل توافيقي" data-language-autonym="العربية" data-language-local-name="Arab" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Combinatoria" title="Combinatoria – Asturia" lang="ast" hreflang="ast" data-title="Combinatoria" data-language-autonym="Asturianu" data-language-local-name="Asturia" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Kombinatorika" title="Kombinatorika – Azerbaijani" lang="az" hreflang="az" data-title="Kombinatorika" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Kuomb%C4%97natuor%C4%97ka" title="Kuombėnatuorėka – Samogitian" lang="sgs" hreflang="sgs" data-title="Kuombėnatuorėka" data-language-autonym="Žemaitėška" data-language-local-name="Samogitian" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9A%D0%B0%D0%BC%D0%B1%D1%96%D0%BD%D0%B0%D1%82%D0%BE%D1%80%D1%8B%D0%BA%D0%B0" title="Камбінаторыка – Belarusia" lang="be" hreflang="be" data-title="Камбінаторыка" data-language-autonym="Беларуская" data-language-local-name="Belarusia" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9A%D0%B0%D0%BC%D0%B1%D1%96%D0%BD%D0%B0%D1%82%D0%BE%D1%80%D1%8B%D0%BA%D0%B0" title="Камбінаторыка – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Камбінаторыка" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BC%D0%B1%D0%B8%D0%BD%D0%B0%D1%82%D0%BE%D1%80%D0%B8%D0%BA%D0%B0" title="Комбинаторика – Bulgaria" lang="bg" hreflang="bg" data-title="Комбинаторика" data-language-autonym="Български" data-language-local-name="Bulgaria" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%97%E0%A7%81%E0%A6%9A%E0%A7%8D%E0%A6%9B-%E0%A6%AC%E0%A6%BF%E0%A6%A8%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%B8%E0%A6%A4%E0%A6%A4%E0%A7%8D%E0%A6%A4%E0%A7%8D%E0%A6%AC" title="গুচ্ছ-বিন্যাসতত্ত্ব – Bengali" lang="bn" hreflang="bn" data-title="গুচ্ছ-বিন্যাসতত্ত্ব" data-language-autonym="বাংলা" data-language-local-name="Bengali" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Kombinatorika" title="Kombinatorika – Bosnia" lang="bs" hreflang="bs" data-title="Kombinatorika" data-language-autonym="Bosanski" data-language-local-name="Bosnia" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Combinat%C3%B2ria" title="Combinatòria – Katalan" lang="ca" hreflang="ca" data-title="Combinatòria" data-language-autonym="Català" data-language-local-name="Katalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Kombinatorika" title="Kombinatorika – Cheska" lang="cs" hreflang="cs" data-title="Kombinatorika" data-language-autonym="Čeština" data-language-local-name="Cheska" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BC%D0%B1%D0%B8%D0%BD%D0%B0%D1%82%D0%BE%D1%80%D0%B8%D0%BA%D0%B0" title="Комбинаторика – Chuvash" lang="cv" hreflang="cv" data-title="Комбинаторика" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Cyfuniadeg" title="Cyfuniadeg – Welsh" lang="cy" hreflang="cy" data-title="Cyfuniadeg" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Kombinatorik" title="Kombinatorik – Dansk" lang="da" hreflang="da" data-title="Kombinatorik" data-language-autonym="Dansk" data-language-local-name="Dansk" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Kombinatorik" title="Kombinatorik – Jerman" lang="de" hreflang="de" data-title="Kombinatorik" data-language-autonym="Deutsch" data-language-local-name="Jerman" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A3%CF%85%CE%BD%CE%B4%CF%85%CE%B1%CF%83%CF%84%CE%B9%CE%BA%CE%AE" title="Συνδυαστική – Yunani" lang="el" hreflang="el" data-title="Συνδυαστική" data-language-autonym="Ελληνικά" data-language-local-name="Yunani" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Combinatorics" title="Combinatorics – Inggris" lang="en" hreflang="en" data-title="Combinatorics" data-language-autonym="English" data-language-local-name="Inggris" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Kombinatoriko" title="Kombinatoriko – Esperanto" lang="eo" hreflang="eo" data-title="Kombinatoriko" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Combinatoria" title="Combinatoria – Spanyol" lang="es" hreflang="es" data-title="Combinatoria" data-language-autonym="Español" data-language-local-name="Spanyol" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Kombinatoorika" title="Kombinatoorika – Esti" lang="et" hreflang="et" data-title="Kombinatoorika" data-language-autonym="Eesti" data-language-local-name="Esti" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Konbinatoria" title="Konbinatoria – Basque" lang="eu" hreflang="eu" data-title="Konbinatoria" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AA%D8%B1%DA%A9%DB%8C%D8%A8%DB%8C%D8%A7%D8%AA" title="ترکیبیات – Persia" lang="fa" hreflang="fa" data-title="ترکیبیات" data-language-autonym="فارسی" data-language-local-name="Persia" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Kombinatoriikka" title="Kombinatoriikka – Suomi" lang="fi" hreflang="fi" data-title="Kombinatoriikka" data-language-autonym="Suomi" data-language-local-name="Suomi" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Combinatoire" title="Combinatoire – Prancis" lang="fr" hreflang="fr" data-title="Combinatoire" data-language-autonym="Français" data-language-local-name="Prancis" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E7%B5%84%E5%90%88%E6%95%B8%E5%AD%B8" title="組合數學 – Gan" lang="gan" hreflang="gan" data-title="組合數學" data-language-autonym="贛語" data-language-local-name="Gan" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Konbinatwar" title="Konbinatwar – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Konbinatwar" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Combinatoria" title="Combinatoria – Galisia" lang="gl" hreflang="gl" data-title="Combinatoria" data-language-autonym="Galego" data-language-local-name="Galisia" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A7%D7%95%D7%9E%D7%91%D7%99%D7%A0%D7%98%D7%95%D7%A8%D7%99%D7%A7%D7%94" title="קומבינטוריקה – Ibrani" lang="he" hreflang="he" data-title="קומבינטוריקה" data-language-autonym="עברית" data-language-local-name="Ibrani" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%95%E0%A5%8D%E0%A4%B0%E0%A4%AE%E0%A4%9A%E0%A4%AF-%E0%A4%B8%E0%A4%82%E0%A4%9A%E0%A4%AF" title="क्रमचय-संचय – Hindi" lang="hi" hreflang="hi" data-title="क्रमचय-संचय" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Kombinatorika" title="Kombinatorika – Kroasia" lang="hr" hreflang="hr" data-title="Kombinatorika" data-language-autonym="Hrvatski" data-language-local-name="Kroasia" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Kombinatorika" title="Kombinatorika – Hungaria" lang="hu" hreflang="hu" data-title="Kombinatorika" data-language-autonym="Magyar" data-language-local-name="Hungaria" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%BF%D5%B8%D5%B4%D5%A2%D5%AB%D5%B6%D5%A1%D5%BF%D5%B8%D6%80%D5%AB%D5%AF%D5%A1" title="Կոմբինատորիկա – Armenia" lang="hy" hreflang="hy" data-title="Կոմբինատորիկա" data-language-autonym="Հայերեն" data-language-local-name="Armenia" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-iba mw-list-item"><a href="https://iba.wikipedia.org/wiki/Kombinatorik" title="Kombinatorik – Iban" lang="iba" hreflang="iba" data-title="Kombinatorik" data-language-autonym="Jaku Iban" data-language-local-name="Iban" class="interlanguage-link-target"><span>Jaku Iban</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Kombinatoriko" title="Kombinatoriko – Ido" lang="io" hreflang="io" data-title="Kombinatoriko" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Talningarfr%C3%A6%C3%B0i" title="Talningarfræði – Islandia" lang="is" hreflang="is" data-title="Talningarfræði" data-language-autonym="Íslenska" data-language-local-name="Islandia" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Combinatoria" title="Combinatoria – Italia" lang="it" hreflang="it" data-title="Combinatoria" data-language-autonym="Italiano" data-language-local-name="Italia" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%B5%84%E5%90%88%E3%81%9B%E6%95%B0%E5%AD%A6" title="組合せ数学 – Jepang" lang="ja" hreflang="ja" data-title="組合せ数学" data-language-autonym="日本語" data-language-local-name="Jepang" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Kambinatuorix" title="Kambinatuorix – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Kambinatuorix" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%99%E1%83%9D%E1%83%9B%E1%83%91%E1%83%98%E1%83%9C%E1%83%90%E1%83%A2%E1%83%9D%E1%83%A0%E1%83%98%E1%83%99%E1%83%90" title="კომბინატორიკა – Georgia" lang="ka" hreflang="ka" data-title="კომბინატორიკა" data-language-autonym="ქართული" data-language-local-name="Georgia" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BC%D0%B1%D0%B8%D0%BD%D0%B0%D1%82%D0%BE%D1%80%D0%B8%D0%BA%D0%B0" title="Комбинаторика – Kazakh" lang="kk" hreflang="kk" data-title="Комбинаторика" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%A1%B0%ED%95%A9%EB%A1%A0" title="조합론 – Korea" lang="ko" hreflang="ko" data-title="조합론" data-language-autonym="한국어" data-language-local-name="Korea" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BC%D0%B1%D0%B8%D0%BD%D0%B0%D1%82%D0%BE%D1%80%D0%B8%D0%BA%D0%B0" title="Комбинаторика – Kirgiz" lang="ky" hreflang="ky" data-title="Комбинаторика" data-language-autonym="Кыргызча" data-language-local-name="Kirgiz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Calculus_coniunctionibus" title="Calculus coniunctionibus – Latin" lang="la" hreflang="la" data-title="Calculus coniunctionibus" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Combinatoria" title="Combinatoria – Lingua Franca Nova" lang="lfn" hreflang="lfn" data-title="Combinatoria" data-language-autonym="Lingua Franca Nova" data-language-local-name="Lingua Franca Nova" class="interlanguage-link-target"><span>Lingua Franca Nova</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Kombinatorika" title="Kombinatorika – Lituavi" lang="lt" hreflang="lt" data-title="Kombinatorika" data-language-autonym="Lietuvių" data-language-local-name="Lituavi" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Kombinatorika" title="Kombinatorika – Latvi" lang="lv" hreflang="lv" data-title="Kombinatorika" data-language-autonym="Latviešu" data-language-local-name="Latvi" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BC%D0%B1%D0%B8%D0%BD%D0%B0%D1%82%D0%BE%D1%80%D0%B8%D0%BA%D0%B0" title="Комбинаторика – Makedonia" lang="mk" hreflang="mk" data-title="Комбинаторика" data-language-autonym="Македонски" data-language-local-name="Makedonia" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BC%D0%B1%D0%B8%D0%BD%D0%B0%D1%82%D0%BE%D1%80%D0%B8%D0%BA" title="Комбинаторик – Mongolia" lang="mn" hreflang="mn" data-title="Комбинаторик" data-language-autonym="Монгол" data-language-local-name="Mongolia" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Kombinatorik" title="Kombinatorik – Melayu" lang="ms" hreflang="ms" data-title="Kombinatorik" data-language-autonym="Bahasa Melayu" data-language-local-name="Melayu" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%80%E1%80%BD%E1%80%94%E1%80%BA%E1%80%98%E1%80%AD%E1%80%AF%E1%80%84%E1%80%BA%E1%80%94%E1%80%90%E1%80%AD%E1%80%AF%E1%80%B8%E1%80%9B%E1%80%85%E1%80%BA" title="ကွန်ဘိုင်နတိုးရစ် – Burma" lang="my" hreflang="my" data-title="ကွန်ဘိုင်နတိုးရစ်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burma" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Combinatoriek" title="Combinatoriek – Belanda" lang="nl" hreflang="nl" data-title="Combinatoriek" data-language-autonym="Nederlands" data-language-local-name="Belanda" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Kombinatorikk" title="Kombinatorikk – Nynorsk Norwegia" lang="nn" hreflang="nn" data-title="Kombinatorikk" data-language-autonym="Norsk nynorsk" data-language-local-name="Nynorsk Norwegia" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Kombinatorikk" title="Kombinatorikk – Bokmål Norwegia" lang="nb" hreflang="nb" data-title="Kombinatorikk" data-language-autonym="Norsk bokmål" data-language-local-name="Bokmål Norwegia" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Kombinatoryka" title="Kombinatoryka – Polski" lang="pl" hreflang="pl" data-title="Kombinatoryka" data-language-autonym="Polski" data-language-local-name="Polski" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Combinat%C3%B3ria" title="Combinatória – Portugis" lang="pt" hreflang="pt" data-title="Combinatória" data-language-autonym="Português" data-language-local-name="Portugis" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Combinatoric%C4%83" title="Combinatorică – Rumania" lang="ro" hreflang="ro" data-title="Combinatorică" data-language-autonym="Română" data-language-local-name="Rumania" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BC%D0%B1%D0%B8%D0%BD%D0%B0%D1%82%D0%BE%D1%80%D0%B8%D0%BA%D0%B0" title="Комбинаторика – Rusia" lang="ru" hreflang="ru" data-title="Комбинаторика" data-language-autonym="Русский" data-language-local-name="Rusia" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BC%D0%B1%D0%B8%D0%BD%D0%B0%D1%82%D0%BE%D1%80%D0%B8%D0%BA%D0%B0" title="Комбинаторика – Sakha" lang="sah" hreflang="sah" data-title="Комбинаторика" data-language-autonym="Саха тыла" data-language-local-name="Sakha" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Kombinatorika" title="Kombinatorika – Serbo-Kroasia" lang="sh" hreflang="sh" data-title="Kombinatorika" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Kroasia" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Combinatorics" title="Combinatorics – Simple English" lang="en-simple" hreflang="en-simple" data-title="Combinatorics" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Kombinatorika" title="Kombinatorika – Slovak" lang="sk" hreflang="sk" data-title="Kombinatorika" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Kombinatorika" title="Kombinatorika – Sloven" lang="sl" hreflang="sl" data-title="Kombinatorika" data-language-autonym="Slovenščina" data-language-local-name="Sloven" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Kombinatorika" title="Kombinatorika – Albania" lang="sq" hreflang="sq" data-title="Kombinatorika" data-language-autonym="Shqip" data-language-local-name="Albania" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BC%D0%B1%D0%B8%D0%BD%D0%B0%D1%82%D0%BE%D1%80%D0%BD%D0%B0_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Комбинаторна математика – Serbia" lang="sr" hreflang="sr" data-title="Комбинаторна математика" data-language-autonym="Српски / srpski" data-language-local-name="Serbia" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Kombinatorik" title="Kombinatorik – Swedia" lang="sv" hreflang="sv" data-title="Kombinatorik" data-language-autonym="Svenska" data-language-local-name="Swedia" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%9A%E0%AF%87%E0%AE%B0%E0%AF%8D%E0%AE%B5%E0%AE%BF%E0%AE%AF%E0%AE%B2%E0%AF%8D_(%E0%AE%95%E0%AE%A3%E0%AE%BF%E0%AE%A4%E0%AE%AE%E0%AF%8D)" title="சேர்வியல் (கணிதம்) – Tamil" lang="ta" hreflang="ta" data-title="சேர்வியல் (கணிதம்)" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%84%E0%B8%93%E0%B8%B4%E0%B8%95%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C%E0%B9%80%E0%B8%8A%E0%B8%B4%E0%B8%87%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%88%E0%B8%B1%E0%B8%94" title="คณิตศาสตร์เชิงการจัด – Thai" lang="th" hreflang="th" data-title="คณิตศาสตร์เชิงการจัด" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Kombinatorika" title="Kombinatorika – Tagalog" lang="tl" hreflang="tl" data-title="Kombinatorika" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Kombinatorik" title="Kombinatorik – Turki" lang="tr" hreflang="tr" data-title="Kombinatorik" data-language-autonym="Türkçe" data-language-local-name="Turki" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BC%D0%B1%D0%B8%D0%BD%D0%B0%D1%82%D0%BE%D1%80%D0%B8%D0%BA%D0%B0" title="Комбинаторика – Tatar" lang="tt" hreflang="tt" data-title="Комбинаторика" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BC%D0%B1%D1%96%D0%BD%D0%B0%D1%82%D0%BE%D1%80%D0%B8%D0%BA%D0%B0" title="Комбінаторика – Ukraina" lang="uk" hreflang="uk" data-title="Комбінаторика" data-language-autonym="Українська" data-language-local-name="Ukraina" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%AA%D8%A7%D9%84%DB%8C%D9%81%DB%8C%D8%A7%D8%AA" title="تالیفیات – Urdu" lang="ur" hreflang="ur" data-title="تالیفیات" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Kombinatorika" title="Kombinatorika – Uzbek" lang="uz" hreflang="uz" data-title="Kombinatorika" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/To%C3%A1n_h%E1%BB%8Dc_t%E1%BB%95_h%E1%BB%A3p" title="Toán học tổ hợp – Vietnam" lang="vi" hreflang="vi" data-title="Toán học tổ hợp" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnam" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E7%BB%84%E5%90%88%E6%95%B0%E5%AD%A6" title="组合数学 – Wu Tionghoa" lang="wuu" hreflang="wuu" data-title="组合数学" data-language-autonym="吴语" data-language-local-name="Wu Tionghoa" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%A7%D7%90%D7%9E%D7%91%D7%99%D7%A0%D7%90%D7%98%D7%90%D7%A8%D7%99%D7%A7" title="קאמבינאטאריק – Yiddish" lang="yi" hreflang="yi" data-title="קאמבינאטאריק" data-language-autonym="ייִדיש" data-language-local-name="Yiddish" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%BB%84%E5%90%88%E6%95%B0%E5%AD%A6" title="组合数学 – Tionghoa" lang="zh" hreflang="zh" data-title="组合数学" data-language-autonym="中文" data-language-local-name="Tionghoa" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%B5%84%E5%90%88%E6%95%B8%E5%AD%B8" title="組合數學 – Kanton" lang="yue" hreflang="yue" data-title="組合數學" data-language-autonym="粵語" data-language-local-name="Kanton" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q76592#sitelinks-wikipedia" title="Sunting pranala interwiki" class="wbc-editpage">Sunting pranala</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Ruang nama"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul 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class="vector-pinnable-header-label">Tampilan</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">pindah ke bilah sisi</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">sembunyikan</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Dari Wikipedia bahasa Indonesia, ensiklopedia bebas</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="id" dir="ltr"><p><b>Kombinatorika</b> adalah cabang <a href="/wiki/Matematika" title="Matematika">matematika</a> yang membahas sifat-sifat dan cara menghitung <a href="/wiki/Struktur_matematika" title="Struktur matematika">struktur-struktur</a> <a href="/wiki/Himpunan_hingga" title="Himpunan hingga">terhingga</a>. Kombinatorika berkaitan erat dengan cabang-cabang matematika lain, dan memiliki banyak penerapan di ilmu <a href="/wiki/Logika" title="Logika">logika</a> sampai <a href="/wiki/Biologi_evolusioner" title="Biologi evolusioner">biologi evolusioner</a> sampai <a href="/wiki/Ilmu_komputer" title="Ilmu komputer">ilmu komputer</a>. Dalam <a href="/wiki/Matematika_murni" title="Matematika murni">matematika murni</a>, permasalahan kombinatorika banyak ditemukan khususnya di <a href="/wiki/Aljabar" title="Aljabar">aljabar</a>, <a href="/wiki/Teori_peluang" title="Teori peluang">teori peluang</a>, <a href="/wiki/Topologi" title="Topologi">topologi</a>, <a href="/wiki/Geometri" title="Geometri">geometri</a>, dan bidang-bidang terapannya.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>Tidak ada kesepakatan umum mengenai cakupan dari ilmu kombinatorika.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Menurut <a href="/w/index.php?title=H.J._Ryser&action=edit&redlink=1" class="new" title="H.J. Ryser (halaman belum tersedia)">H.J. Ryser</a>, definisi ilmu ini sulit karena berurusan dengan sangat banyak [sub]cabang matematika.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Cakupan kombinatorika dapat dideskripsikan lewat tipe-tipe masalah yang dikerjakan: </p> <ul><li><i>Mencacah</i> (enumerasi) banyaknya struktur atau susunan yang berkaitan dengan sistem hingga,</li> <li>Menentukan <i>keberadaan</i> struktur yang memenuhi kriteria-kriteria yang diinginkan,</li> <li><i>Membuat</i> (mengonstruksi) struktur-struktur tersebut, mungkin dalam banyak cara, dan</li> <li>Melakukan <i>optimisasi</i> untuk mendapatkan struktur atau solusi "terbaik" dari satu atau beberapa kriteria; sebagai contoh "terbesar" atau "terkecil".</li></ul> <p>Walaupun berfokus pada sistem hingga, beberapa permasalahan dan teknik kombinatorika dapat diperumum ke bentuk tak hingga (yang <a href="/wiki/Matematika_diskrit" title="Matematika diskrit">diskret</a> dan <a href="/wiki/Himpunan_terhitung" title="Himpunan terhitung">terhitung</a>). </p><p>Banyak permasalahan kombinatorika pada awalnya muncul secara terisolasi, mengakibatkan banyak solusi-solusi <i>ad hoc</i> (spesifik) tergantung konteks pembahasan. Tapi pada akhir abad ke-20, konsep teoritis kombinatorika dikembangkan dan membuat kombinatorika menjadi cabang matematika terpisah.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Referensi">Referensi</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kombinatorika&veaction=edit&section=1" title="Sunting bagian: Referensi" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kombinatorika&action=edit&section=1" title="Sunting kode sumber bagian: Referensi"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text">Björner and Stanley, p. 2</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite class="citation web">Pak, Igor. <a rel="nofollow" class="external text" href="//www.math.ucla.edu/~pak/hidden/papers/Quotes/Combinatorics-quotes.htm">"What is Combinatorics?"</a><span class="reference-accessdate">. Diakses tanggal <span class="nowrap">1 November</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=What+is+Combinatorics%3F&rft.aulast=Pak&rft.aufirst=Igor&rft_id=%2F%2Fwww.math.ucla.edu%2F~pak%2Fhidden%2Fpapers%2FQuotes%2FCombinatorics-quotes.htm&rfr_id=info%3Asid%2Fid.wikipedia.org%3AKombinatorika" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><a href="#CITEREFRyser1963">Ryser 1963</a>, p. 2</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><cite class="citation book">Lovász, László (1979). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=ueq1CwAAQBAJ&pg=PP1"><i>Combinatorial Problems and Exercises</i></a>. North-Holland. <a href="/wiki/International_Standard_Book_Number" class="mw-redirect" title="International Standard Book Number">ISBN</a> <a href="/wiki/Istimewa:Sumber_buku/9780821842621" title="Istimewa:Sumber buku/9780821842621">9780821842621</a>. <q>In my opinion, combinatorics is now growing out of this early stage.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Combinatorial+Problems+and+Exercises&rft.pub=North-Holland&rft.date=1979&rft.isbn=9780821842621&rft.aulast=Lov%C3%A1sz&rft.aufirst=L%C3%A1szl%C3%B3&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dueq1CwAAQBAJ%26pg%3DPP1&rfr_id=info%3Asid%2Fid.wikipedia.org%3AKombinatorika" class="Z3988"><span style="display:none;"> </span></span></span> </li> </ol> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r23782733">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output 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style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4164746-4">Integrated Authority File (Jerman)</a></span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Perpustakaan nasional</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="uid"><a rel="nofollow" class="external text" href="http://catalogo.bne.es/uhtbin/authoritybrowse.cgi?action=display&authority_id=XX525029">Spanyol</a></span></li> <li><span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb119470231">Prancis</a> <a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb119470231">(data)</a></span></li> <li><span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/subjects/sh85028802">Amerika Serikat</a></span></li> <li><span class="uid"><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=ph121739&CON_LNG=ENG">Republik Ceko</a></span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Lain-lain</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://academic.microsoft.com/v2/detail/114614502">Microsoft Academic</a></span></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r23782733"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r25847331"></div><div role="navigation" class="navbox" aria-labelledby="Matematika_(Bidang_matematika)" style="padding:3px"><table class="nowraplinks mw-collapsible expanded navbox-inner" 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class="navbox-group" style="width:1%"><a href="/wiki/Fondasi_matematika" title="Fondasi matematika">Fondasi</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Filsafat_matematika" title="Filsafat matematika">Filsafat matematika</a></li> <li><a href="/wiki/Logika_matematika" title="Logika matematika">Logika matematika</a></li> <li><a href="/wiki/Teori_himpunan" title="Teori himpunan">Teori himpunan</a></li> <li><a href="/wiki/Teori_informasi" title="Teori informasi">Teori informasi</a></li> <li><a href="/wiki/Teori_kategori" title="Teori kategori">Teori kategori</a></li> <li><a href="/w/index.php?title=Teori_tipe&action=edit&redlink=1" class="new" title="Teori tipe (halaman belum tersedia)">Teori tipe</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Aljabar" title="Aljabar">Aljabar</a></th><td class="navbox-list-with-group 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dinamis">Teori sistem dinamis</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Matematika_diskret" class="mw-redirect" title="Matematika diskret">Diskret</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a class="mw-selflink selflink">Kombinatorika</a></li> <li><a href="/wiki/Teori_graf" title="Teori graf">Teori graf</a></li> <li><a href="/wiki/Teori_order" title="Teori order">Teori order</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Geometri" title="Geometri">Geometri</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Geometri_aljabar" title="Geometri aljabar">Aljabar</a></li> <li><a href="/wiki/Geometri_analitis" title="Geometri analitis">Analitis</a></li> <li><a href="/wiki/Geometri_diferensial" title="Geometri diferensial">Diferensial</a></li> <li><a href="/wiki/Geometri_diskrit" title="Geometri diskrit">Diskrit</a></li> <li><a href="/wiki/Geometri_Euklides" title="Geometri Euklides">Euklides</a></li> <li><a href="/wiki/Geometri_hingga" title="Geometri hingga">Hingga</a></li> <li><a href="/wiki/Trigonometri" title="Trigonometri">Trigonometri</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Matematika_komputasi" title="Matematika komputasi">Komputasi</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Analisis_numerik" title="Analisis numerik">Analisis numerik</a> (<a href="/wiki/Daftar_topik_analisis_numerik" title="Daftar topik analisis numerik">Topik</a>)</li> <li><a href="/wiki/Ilmu_komputer" title="Ilmu komputer">Ilmu komputer</a></li> <li><a href="/w/index.php?title=Komputasi_simbolik&action=edit&redlink=1" class="new" title="Komputasi simbolik (halaman belum tersedia)">Komputasi simbolik</a></li> <li><a href="/wiki/Teori_komputasi" title="Teori komputasi">Teori komputasi</a></li> <li><a href="/w/index.php?title=Teori_kompleksitas_komputasi&action=edit&redlink=1" class="new" title="Teori kompleksitas komputasi (halaman belum tersedia)">Teori kompleksitas komputasi</a></li> <li><a href="/wiki/Optimisasi" title="Optimisasi">Optimisasi matematika</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Teori_bilangan" title="Teori bilangan">Teori bilangan</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Aritmetika" title="Aritmetika">Aritmetika</a></li> <li><a href="/w/index.php?title=Geometri_Diophantine&action=edit&redlink=1" class="new" title="Geometri Diophantine (halaman belum tersedia)">Geometri Diophantine</a></li> <li><a href="/wiki/Teori_bilangan_aljabar" title="Teori bilangan aljabar">Teori bilangan aljabar</a></li> <li><a href="/w/index.php?title=Teori_bilangan_analitis&action=edit&redlink=1" class="new" title="Teori bilangan analitis (halaman belum tersedia)">Teori bilangan analitis</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Topologi" title="Topologi">Topologi</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/w/index.php?title=Teori_homotopi&action=edit&redlink=1" class="new" title="Teori homotopi (halaman belum tersedia)">Teori homotopi</a></li> <li><a href="/wiki/Topologi_aljabar" title="Topologi aljabar">Aljabar</a></li> <li><a href="/w/index.php?title=Topologi_diferensial&action=edit&redlink=1" class="new" title="Topologi diferensial (halaman belum tersedia)">Diferensial</a></li> <li><a href="/w/index.php?title=Topologi_geometris&action=edit&redlink=1" class="new" title="Topologi geometris (halaman belum tersedia)">Geometris</a></li> <li><a href="/wiki/Topologi_umum" title="Topologi umum">Umum</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Matematika_terapan" title="Matematika terapan">Terapan</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Biologi_matematika_dan_teori" title="Biologi matematika dan teori">Matematika biologi</a></li> <li><a href="/wiki/Matematika_ekonomi" title="Matematika ekonomi">Matematika ekonomi</a></li> <li><a href="/wiki/Matematika_keuangan" title="Matematika keuangan">Matematika keuangan</a></li> <li><a href="/wiki/Fisika_matematis" title="Fisika matematis">Fisika matematis</a></li> <li><a href="/wiki/Kimia_matematika" title="Kimia matematika">Kimia matematika</a></li> <li><a href="/w/index.php?title=Psikologi_matematis&action=edit&redlink=1" class="new" title="Psikologi matematis (halaman belum tersedia)">Psikologi matematis</a></li> <li><a href="/wiki/Statistika" title="Statistika">Statistika</a></li> <li><a href="/wiki/Statistika_matematika" title="Statistika matematika">Statistika matematika</a></li> <li><a href="/wiki/Teori_peluang" title="Teori peluang">Teori peluang</a></li> <li><a href="/wiki/Ilmu_sistem" title="Ilmu sistem">Ilmu sistem</a> (<a href="/w/index.php?title=Teori_kendali&action=edit&redlink=1" class="new" title="Teori kendali (halaman belum tersedia)">Teori kendali</a>, <a href="/wiki/Teori_permainan" title="Teori permainan">Teori permainan</a>, <a href="/wiki/Riset_operasi" title="Riset operasi">Riset operasi</a>)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Divisi</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Matematika_murni" title="Matematika murni">Matematika murni</a></li> <li><a href="/wiki/Matematika_terapan" title="Matematika terapan">Matematika terapan</a></li> <li><a href="/wiki/Matematika_diskret" class="mw-redirect" title="Matematika diskret">Matematika diskret</a></li> <li><a href="/wiki/Matematika_komputasi" title="Matematika komputasi">Matematika komputasi</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Topik terkait</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Matematika_dan_seni" title="Matematika dan seni">Matematika dan seni</a></li> <li><a href="/wiki/Matematika_rekreasi" title="Matematika rekreasi">Matematika rekreasi</a></li> <li><a href="/wiki/Pendidikan_matematika" title="Pendidikan matematika">Pendidikan matematika</a></li> <li><a href="/wiki/Sejarah_matematika" title="Sejarah matematika">Sejarah 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rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r25847331"></div><div role="navigation" class="navbox authority-control" aria-labelledby="Pengawasan_otoritas_frameless_&#124;text-top_&#124;10px_&#124;alt=Sunting_ini_di_Wikidata_&#124;link=https&#58;//www.wikidata.org/wiki/Q76592#identifiers&#124;Sunting_ini_di_Wikidata" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Pengawasan_otoritas_frameless_&#124;text-top_&#124;10px_&#124;alt=Sunting_ini_di_Wikidata_&#124;link=https&#58;//www.wikidata.org/wiki/Q76592#identifiers&#124;Sunting_ini_di_Wikidata" style="font-size:114%;margin:0 4em"><a href="/wiki/Bantuan:Pengawasan_otoritas" title="Bantuan:Pengawasan otoritas">Pengawasan otoritas</a> <span class="mw-valign-text-top" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q76592#identifiers" title="Sunting ini di Wikidata"><img alt="Sunting ini di Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Umum</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4164746-4">Integrated Authority File (Jerman)</a></span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Perpustakaan nasional</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="uid"><a rel="nofollow" class="external text" href="http://catalogo.bne.es/uhtbin/authoritybrowse.cgi?action=display&authority_id=XX525029">Spanyol</a></span></li> <li><span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb119470231">Prancis</a> <a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb119470231">(data)</a></span></li> <li><span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/subjects/sh85028802">Amerika Serikat</a></span></li> <li><span class="uid"><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=ph121739&CON_LNG=ENG">Republik Ceko</a></span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Lain-lain</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://academic.microsoft.com/v2/detail/114614502">Microsoft Academic</a></span></li></ul> </div></td></tr></tbody></table></div> <p><br /> </p> <style data-mw-deduplicate="TemplateStyles:r18342415">.mw-parser-output .asbox{position:relative;overflow:hidden}.mw-parser-output .asbox table{background:transparent}.mw-parser-output .asbox p{margin:0}.mw-parser-output .asbox p+p{margin-top:0.25em}.mw-parser-output .asbox-body{font-style:italic}.mw-parser-output .asbox-note{font-size:smaller}.mw-parser-output .asbox .navbar{position:absolute;top:-0.75em;right:1em;display:none}</style><div 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