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× 2!) çıkarılır.","Sonuç olarak Ali ve Veli yan yana olmama durumu 7! - 2 × 6! × 2! olarak bulunur."]},"beginTime":312,"endTime":468,"href":"/video/preview/15882785625168109559?parent-reqid=1751697572077319-5094035101624255807-balancer-l7leveler-kubr-yp-klg-80-BAL&text=Olasilik+SORU+%C3%87%C3%B6z%C3%BCm%C3%BC+2+%7C+YGS+Kampi+%2716+Matematik&t=312&ask_summarization=1"},{"index":4,"title":"Yuvarlak Masa Etrafında Sıralama Problemi","list":{"type":"unordered","items":["Dört kişi yuvarlak masa etrafında sıralanacak ve üç faktöriyel (3!) hesaplanacak.","İki kişi yan yana oturacak ve bunların yer değiştirmesi için iki faktöriyel (2!) hesaplanacak.","Yan yana oturan kişilerin yer değiştirmesi, yuvarlak masa etrafında oturmayan kişilerin yer değiştirmesinden farklıdır."]},"beginTime":470,"endTime":506,"href":"/video/preview/15882785625168109559?parent-reqid=1751697572077319-5094035101624255807-balancer-l7leveler-kubr-yp-klg-80-BAL&text=Olasilik+SORU+%C3%87%C3%B6z%C3%BCm%C3%BC+2+%7C+YGS+Kampi+%2716+Matematik&t=470&ask_summarization=1"},{"index":5,"title":"Yedi Basamaklı Permütasyon Problemi","list":{"type":"unordered","items":["Yedi basamaklı, tekrarlı permütasyon problemi çözülüyor: 7! / (3! × 2!)","Sıfırla başlayan yedi basamaklı sayılar olmaz, bu nedenle ilk basamak sıfır olamaz.","Sıfır hariç beş rakamla başlanabilir, bu nedenle 5/7 oranında sıfırla başlayan sayılar olmaz."]},"beginTime":506,"endTime":585,"href":"/video/preview/15882785625168109559?parent-reqid=1751697572077319-5094035101624255807-balancer-l7leveler-kubr-yp-klg-80-BAL&text=Olasilik+SORU+%C3%87%C3%B6z%C3%BCm%C3%BC+2+%7C+YGS+Kampi+%2716+Matematik&t=506&ask_summarization=1"},{"index":6,"title":"Alternatif Çözüm Yöntemi","list":{"type":"unordered","items":["Yedi rakam sıralanır ve ilk basamak için beş farklı seçenek vardır.","İlk basamak 2 olduğunda, geriye kalan altı rakamdan iki tanesi 2, bir tanesi 7 ve bir tanesi 9 olabilir.","Bu durumda 5! / (2! × 3! × 2!) hesaplaması yapılır."]},"beginTime":585,"endTime":696,"href":"/video/preview/15882785625168109559?parent-reqid=1751697572077319-5094035101624255807-balancer-l7leveler-kubr-yp-klg-80-BAL&text=Olasilik+SORU+%C3%87%C3%B6z%C3%BCm%C3%BC+2+%7C+YGS+Kampi+%2716+Matematik&t=585&ask_summarization=1"},{"index":7,"title":"Son Çözüm Yöntemi","list":{"type":"unordered","items":["Üç rakamdan sonra dört rakam gelir ve bu durumda 8 faktöriyel hesaplanır.","Üç faktöriyel ve iki faktöriyel ile bölünür.","Sonuç olarak 8! 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Öğretmen ve Tonguç adlı öğrencisi arasında soru-cevap şeklinde ilerleyen bir ders anlatımı yer almaktadır.","Videoda permütasyon konusu detaylı bir şekilde ele alınmaktadır. İlk bölümde tekrarlı permütasyon kavramı, mavi, kırmızı ve beyaz bilyeler üzerinden örneklerle açıklanmakta, ardından yuvarlak masa soruları ve anahtarlık soruları için formüller verilmektedir. İkinci bölümde ise yuvarlak masa etrafında oturan kişilerin yer değiştirme durumları ve yedi basamaklı tekrarlı permütasyon problemleri adım adım çözülmektedir.","Videoda ayrıca Ali ve Veli'nin yan yana oturmamak koşuluyla yuvarlak masa etrafında kaç farklı biçimde oturabileceği gibi pratik problemler ve sıfırın basamakta yer alması durumunda permütasyon hesaplamaları da detaylı olarak açıklanmaktadır."]},"endTime":853,"title":"Matematik Dersi: Permütasyon Konusu","beginTime":0}],"fullResult":[{"index":0,"title":"Tekrarlı Permütasyon","list":{"type":"unordered","items":["Malatya kelimesinde tekrar eden harfler var ve bu tekrarlı permütasyon konusunu hatırlatıyor.","Tekrarlı permütasyon formülü: n faktöriyel bölü tekrar eden harflerin faktöriyel çarpı diğer harflerin faktöriyel çarpı...","Örnek olarak 3 özdeş mavi top, 4 özdeş kırmızı top ve 2 özdeş beyaz top toplam 9 farklı şekilde sıralanabilir, ancak özdeşler ayırt edilemediği için 9! / (3! × 4! × 2!) şeklinde hesaplanır."]},"beginTime":33,"endTime":121,"href":"/video/preview/15882785625168109559?parent-reqid=1751697572077319-5094035101624255807-balancer-l7leveler-kubr-yp-klg-80-BAL&text=Olasilik+SORU+%C3%87%C3%B6z%C3%BCm%C3%BC+2+%7C+YGS+Kampi+%2716+Matematik&t=33&ask_summarization=1"},{"index":1,"title":"Tekrarlı Permütasyon Uygulaması","list":{"type":"unordered","items":["\"Malatya\" kelimesinde 3 tane \"a\" harfi var ve M harfi ile başlayıp A harfi ile biten kelimelerin sayısı soruluyor.","M harfi ile başlayıp A harfi ile biten kelimelerin sayısı: 5! / (2! × 1! × 1!) = 60 olarak hesaplanır."]},"beginTime":121,"endTime":193,"href":"/video/preview/15882785625168109559?parent-reqid=1751697572077319-5094035101624255807-balancer-l7leveler-kubr-yp-klg-80-BAL&text=Olasilik+SORU+%C3%87%C3%B6z%C3%BCm%C3%BC+2+%7C+YGS+Kampi+%2716+Matematik&t=121&ask_summarization=1"},{"index":2,"title":"Yuvarlak Masa ve Anahtarlık Soruları","list":{"type":"unordered","items":["Yuvarlak masa sorularında n faktöriyel bölü (n-1)! formülü kullanılır, çünkü bir kişi sabitlenir ve sağına ve soluna sıralama yapılır.","Anahtarlık maskotsuz sorularında n faktöriyel bölü 2 formülü kullanılır, çünkü anahtarlık çevrilebilir ve sağdan soldan sıralama aynı olur.","Anahtarlık maskotlu sorularında n faktöriyel bölü (n-1) formülü kullanılır."]},"beginTime":193,"endTime":312,"href":"/video/preview/15882785625168109559?parent-reqid=1751697572077319-5094035101624255807-balancer-l7leveler-kubr-yp-klg-80-BAL&text=Olasilik+SORU+%C3%87%C3%B6z%C3%BCm%C3%BC+2+%7C+YGS+Kampi+%2716+Matematik&t=193&ask_summarization=1"},{"index":3,"title":"Ali ve Veli Yan Yana Oturmama Koşulu","list":{"type":"unordered","items":["Ali ve Veli yan yana oturmamak kaydıyla 8 kişi yuvarlak masaya nasıl oturabilir sorusu çözülüyor.","Önce tüm durumlar (7!) hesaplanır, sonra Ali ve Veli yan yana olma durumları (2 × 6! 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