{"id":1023,"date":"2023-07-27T23:10:51","date_gmt":"2023-07-27T23:10:51","guid":{"rendered":"https:\/\/statorials.org\/tr\/cok-terimli-katsayi\/"},"modified":"2023-07-27T23:10:51","modified_gmt":"2023-07-27T23:10:51","slug":"cok-terimli-katsayi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/cok-terimli-katsayi\/","title":{"rendered":"\u00c7ok terimli katsay\u0131: tan\u0131m ve \u00f6rnekler"},"content":{"rendered":"

<\/p>\n

\n

\u00c7ok terimli bir katsay\u0131,<\/strong> n<\/em> nesnenin n 1<\/sub><\/em> , n 2<\/sub><\/em> , \u2026, n k<\/sub><\/em> boyutunda k<\/em> gruba olas\u0131 b\u00f6l\u00fcmleme say\u0131s\u0131n\u0131 tan\u0131mlar.<\/span><\/p>\n

\u00c7ok terimli bir katsay\u0131y\u0131 hesaplamak i\u00e7in form\u00fcl \u015f\u00f6yledir:<\/span><\/p>\n

\u00c7ok terimli katsay\u0131 = n! \/ (n 1<\/sub> ! * n 2<\/sub> ! * \u2026 * nk<\/sub> !)<\/span><\/p>\n

A\u015fa\u011f\u0131daki \u00f6rnekler, multinom katsay\u0131s\u0131n\u0131n pratikte nas\u0131l hesaplanaca\u011f\u0131n\u0131 g\u00f6stermektedir.<\/span><\/p>\n

\u00d6rnek 1: bir kelimedeki harfler<\/strong><\/span><\/h3>\n

ARKANSAS kelimesinin ka\u00e7 tane benzersiz b\u00f6l\u00fcm\u00fc vard\u0131r?<\/span><\/p>\n

\u00c7\u00f6z\u00fcm:<\/strong> A\u015fa\u011f\u0131daki de\u011ferleri \u00e7ok terimli katsay\u0131 form\u00fcl\u00fcne kolayca yerle\u015ftirebiliriz:<\/span><\/p>\n

n<\/strong> (toplam harfler): 8<\/span><\/p>\n

n 1<\/sub><\/strong> (\u201cA\u201d harfi): 3<\/span><\/p>\n

n 2<\/sub><\/strong> (\u201cR\u201d harfi): 1<\/span><\/p>\n

n 3<\/sub><\/strong> (\u201cK\u201d harfi): 1<\/span><\/p>\n

n 4<\/sub><\/strong> (\u201cN\u201d harfi): 1<\/span><\/p>\n

n 5<\/sub><\/strong> (\u201cS\u201d harfi): 2<\/span><\/p>\n

\u00c7ok terimli katsay\u0131 = 8! \/ (3! * 1! * 1! * 1! * 2!) = 3.360<\/strong><\/span><\/p>\n

ARKANSAS kelimesinin 3.360<\/strong> benzersiz b\u00f6l\u00fcm\u00fc vard\u0131r.<\/span><\/p>\n

\u00d6rnek 2: Okul y\u0131l\u0131 ba\u015f\u0131na \u00f6\u011frenciler<\/strong><\/span><\/h3>\n

Alt\u0131 ki\u015filik bir grup, 3 son s\u0131n\u0131f, 2 \u00fc\u00e7\u00fcnc\u00fc ve 1 ikinci s\u0131n\u0131ftan olu\u015fur. Bu \u00f6\u011frenci grubundan seviye ba\u015f\u0131na ka\u00e7 benzersiz puan var?<\/span><\/p>\n

\u00c7\u00f6z\u00fcm:<\/strong> A\u015fa\u011f\u0131daki de\u011ferleri \u00e7ok terimli katsay\u0131 form\u00fcl\u00fcne kolayca yerle\u015ftirebiliriz:<\/span><\/p>\n

n<\/strong> (toplam \u00f6\u011frenci): 6<\/span><\/p>\n

n 1<\/sub><\/strong> (toplam son s\u0131n\u0131f \u00f6\u011frencileri): 3<\/span><\/p>\n

n 2<\/sub><\/strong> (gen\u00e7lerin toplam\u0131): 2<\/span><\/p>\n

n 3<\/sub><\/strong> (toplam ikinci s\u0131n\u0131f \u00f6\u011frencileri): 1<\/span><\/p>\n

\u00c7ok terimli katsay\u0131 = 6! \/ (3! * 2! * 1!) = 60<\/strong><\/span><\/p>\n

Bu \u00f6\u011frencilerin seviye ba\u015f\u0131na 60<\/strong> benzersiz puan\u0131 vard\u0131r.<\/span><\/p>\n

\u00d6rnek 3: Siyasi parti tercihi<\/strong><\/span><\/h3>\n

Belirli bir il\u00e7ede ya\u015fayan on ki\u015fiden olu\u015fan bir gruptan 3’\u00fc Cumhuriyet\u00e7i, 5’i Demokrat ve 2’si ba\u011f\u0131ms\u0131zd\u0131r. Bu yerle\u015fik grubun siyasi partilere g\u00f6re ka\u00e7 tane benzersiz b\u00f6l\u00fcm\u00fc vard\u0131r?<\/span><\/p>\n

\u00c7\u00f6z\u00fcm:<\/strong> A\u015fa\u011f\u0131daki de\u011ferleri \u00e7ok terimli katsay\u0131 form\u00fcl\u00fcne kolayca yerle\u015ftirebiliriz:<\/span><\/p>\n

n<\/strong> (toplam sakin): 10<\/span><\/p>\n

n 1<\/sub><\/strong> (toplam Cumhuriyet\u00e7iler): 3<\/span><\/p>\n

2<\/sub> numara<\/strong> (toplam Demokratlar): 5<\/span><\/p>\n

n 3<\/sub><\/strong> (toplam Ba\u011f\u0131ms\u0131zlar): 2<\/span><\/p>\n

\u00c7ok terimli katsay\u0131 = 10! \/ (3! * 5! * 2!) = 2,520<\/strong><\/span><\/p>\n

Bu sakinlerin siyasi partilere g\u00f6re 2.520<\/strong> benzersiz d\u00f6k\u00fcm\u00fc bulunmaktad\u0131r.<\/span><\/p>\n

Ek kaynaklar<\/strong><\/span><\/h3>\n

\u00c7ok terimli katsay\u0131, her sonucun sabit bir ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131na sahip oldu\u011fu k<\/em> farkl\u0131 sonu\u00e7 i\u00e7in belirli say\u0131da say\u0131m elde etme olas\u0131l\u0131\u011f\u0131n\u0131 tan\u0131mlayan \u00e7ok terimli da\u011f\u0131l\u0131m<\/a> form\u00fcl\u00fcn\u00fcn bir b\u00f6l\u00fcm\u00fcnde kullan\u0131l\u0131r.<\/span><\/p>\n

Bonus:<\/strong> \u00c7ok terimli katsay\u0131lar\u0131 kolayca hesaplamak i\u00e7in \u00c7ok Terimli Katsay\u0131lar Hesaplay\u0131c\u0131y\u0131 kullanabilirsiniz.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

\u00c7ok terimli bir katsay\u0131, n nesnenin n 1 , n 2 , \u2026, n k boyutunda k gruba olas\u0131 b\u00f6l\u00fcmleme say\u0131s\u0131n\u0131 tan\u0131mlar. \u00c7ok terimli bir katsay\u0131y\u0131 hesaplamak i\u00e7in form\u00fcl \u015f\u00f6yledir: \u00c7ok terimli katsay\u0131 = n! \/ (n 1 ! * n 2 ! * \u2026 * nk !) A\u015fa\u011f\u0131daki \u00f6rnekler, multinom katsay\u0131s\u0131n\u0131n pratikte nas\u0131l hesaplanaca\u011f\u0131n\u0131 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-1023","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"\n\u00c7ok terimli katsay\u0131: tan\u0131m ve \u00f6rnekler - Statorials<\/title>\n<meta name=\"description\" content=\"Bir tan\u0131m ve birka\u00e7 \u00f6rnek i\u00e7eren, \u00e7ok terimli bir katsay\u0131n\u0131n basit bir a\u00e7\u0131klamas\u0131.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/tr\/cok-terimli-katsayi\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u00c7ok terimli katsay\u0131: tan\u0131m ve \u00f6rnekler - Statorials\" \/>\n<meta property=\"og:description\" content=\"Bir tan\u0131m ve birka\u00e7 \u00f6rnek i\u00e7eren, \u00e7ok terimli bir katsay\u0131n\u0131n basit bir a\u00e7\u0131klamas\u0131.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/tr\/cok-terimli-katsayi\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-27T23:10:51+00:00\" \/>\n<meta name=\"author\" content=\"Dr.benjamin anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Yazan:\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr.benjamin anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tahmini okuma s\u00fcresi\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 dakika\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/tr\/cok-terimli-katsayi\/\",\"url\":\"https:\/\/statorials.org\/tr\/cok-terimli-katsayi\/\",\"name\":\"\u00c7ok terimli katsay\u0131: tan\u0131m ve \u00f6rnekler - Statorials\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/tr\/#website\"},\"datePublished\":\"2023-07-27T23:10:51+00:00\",\"dateModified\":\"2023-07-27T23:10:51+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\"},\"description\":\"Bir tan\u0131m ve birka\u00e7 \u00f6rnek i\u00e7eren, \u00e7ok terimli bir katsay\u0131n\u0131n basit bir a\u00e7\u0131klamas\u0131.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/tr\/cok-terimli-katsayi\/#breadcrumb\"},\"inLanguage\":\"tr\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/tr\/cok-terimli-katsayi\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/tr\/cok-terimli-katsayi\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Ev\",\"item\":\"https:\/\/statorials.org\/tr\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u00c7ok terimli katsay\u0131: tan\u0131m ve \u00f6rnekler\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/tr\/#website\",\"url\":\"https:\/\/statorials.org\/tr\/\",\"name\":\"Statorials\",\"description\":\"\u0130statistik okuryazarl\u0131\u011f\u0131 rehberiniz!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/tr\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"tr\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\",\"name\":\"Dr.benjamin anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"tr\",\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Dr.benjamin anderson\"},\"description\":\"Merhaba, ben Benjamin, emekli bir istatistik profes\u00f6r\u00fc ve Statorials \u00f6\u011fretmenine d\u00f6n\u00fc\u015ft\u00fcm. \u0130statistik alan\u0131ndaki kapsaml\u0131 deneyimim ve uzmanl\u0131\u011f\u0131mla, \u00f6\u011frencilerimi Statorials arac\u0131l\u0131\u011f\u0131yla g\u00fc\u00e7lendirmek i\u00e7in bilgilerimi payla\u015fmaya can at\u0131yorum. 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