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10'a Matematik 👉 https://bit.ly/3zqTTJF Dinamo Matematik 👉 https://bit.ly/2XySOT8 📌Tonguç Plus ile Hedeflerinde En Üste Ulaş! 👉 https://bit.ly/2Zie3JI 10.sınıf matematik 2018-2019 güncel...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3046380/03852f24572cac8494bdb877931ea478/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/JMssPgEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"14","reqid":"1771672292170350-14258962204892842461-balancer-l7leveler-kubr-yp-sas-167-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1771672292170350-14258962204892842461-balancer-l7leveler-kubr-yp-sas-167-BAL&text=videoid:15305128301600373089","teaser":[{"list":{"type":"unordered","items":["Bu video, bir matematik öğretmeninin Tonguç Akademi platformunda sayma, permütasyon ve kombinasyon konularını anlattığı kapsamlı bir eğitim içeriğidir. Öğretmen, kendisini \"kovanın kovası\" olarak tanımlamakta ve öğrencilere adım adım konuları açıklamaktadır.","Video, sayma prensipleri ile başlayıp faktöriyel hesaplamalarına geçmekte, ardından permütasyon konusunu detaylı olarak ele almaktadır. Tekrarlı permütasyon formülü, kombinasyon ve binom olasılık gibi konular da videoda işlenmektedir. İçerik, teorik açıklamaların yanı sıra çeşitli örnek sorular ve pratik çözümlerle desteklenmektedir.","Videoda a'dan b'ye yol hesaplamaları, kitapların dizilmesi, kelime oluşturma, oyuncakların dağıtılması gibi günlük hayattan örnekler üzerinden konular pekiştirilmektedir. Ayrıca, öğrencilerin yazılı sınavlarına hazırlık için gerekli olan faktöriyel, permütasyon ve kombinasyon problemlerinin çözüm yöntemleri detaylı olarak gösterilmektedir."]},"endTime":5646,"title":"Matematik Dersi: Sayma, Permütasyon ve Kombinasyon","beginTime":0}],"fullResult":[{"index":0,"title":"Yatay ve Düşey Yol Hesaplaması","list":{"type":"unordered","items":["A'dan B'ye yatay ve düşey yol hesaplaması yapılıyor, B noktasını geçmemek gerekiyor.","Toplam yol sayısı hesaplanıyor: 1+1=2, 2+1=3, 3+1=4, 4+1=5, 1+2=3, 3+3=6, 6+4=10, 10+5=15 farklı şekilde."]},"beginTime":0,"endTime":33,"href":"/video/preview/15305128301600373089?parent-reqid=1771672292170350-14258962204892842461-balancer-l7leveler-kubr-yp-sas-167-BAL&text=THATSAHAZARD10&t=0&ask_summarization=1"},{"index":1,"title":"Tonguç Akademi Hizmetleri","list":{"type":"unordered","items":["Tonguç Akademi'de olası tüm soru çeşitleri sunuluyor ve bu sene bomba gibi hazırlanmışlar.","10. sınıfta canlı yayınlar olacak ve Tonguç üniversitede bile yardımcı oluyor.","Sıfırdan 10. sınıf serisinde kimya, biyoloji, fizik, tarih, coğrafya, matematik ve Türk dili ve edebiyat konuları bulunuyor.","Kitapta Anadolu Lisesi, Fen Lisesi veya herhangi bir ayrım yapılmadan tüm liseler için içerikler sunuluyor."]},"beginTime":33,"endTime":114,"href":"/video/preview/15305128301600373089?parent-reqid=1771672292170350-14258962204892842461-balancer-l7leveler-kubr-yp-sas-167-BAL&text=THATSAHAZARD10&t=33&ask_summarization=1"},{"index":2,"title":"Tonguç Akademi Üyeliği ve Canlı Test","list":{"type":"unordered","items":["Tonguç Akademi üyeliği ücretsiz.","Canlı test çözmek için akademiye girip matematik, sayma ve olasılık, saymanın temel prensipleri, konu testleri ve canlı test sıralamasıyla erişilebilir.","Canlı testte öğrencilerin cevapları gösteriliyor ve hızlı cevap verenler tebrik ediliyor."]},"beginTime":114,"endTime":286,"href":"/video/preview/15305128301600373089?parent-reqid=1771672292170350-14258962204892842461-balancer-l7leveler-kubr-yp-sas-167-BAL&text=THATSAHAZARD10&t=114&ask_summarization=1"},{"index":3,"title":"Canlı Test Soruları","list":{"type":"unordered","items":["İlk soruda A'dan C'ye gidişte kullanılan yollar dönüşte kullanılmamak koşuluyla kaç parça ile gidiş dönüş yapılabilir sorusu çözülüyor.","İkinci soruda dört çikolata ve altı meyveli pasta vitrine dizilirken meyveli pastalar yan yana olmamak koşulu ile kaç farklı şekilde dizilebileceği hesaplanıyor.","Üçüncü soruda 6!+7!÷9!×8! işleminin sonucu bulunuyor."]},"beginTime":286,"endTime":535,"href":"/video/preview/15305128301600373089?parent-reqid=1771672292170350-14258962204892842461-balancer-l7leveler-kubr-yp-sas-167-BAL&text=THATSAHAZARD10&t=286&ask_summarization=1"},{"index":4,"title":"Ödüllü Soru","list":{"type":"unordered","items":["Ödüllü soruda abc birer pozitif tam sayı toplamları 8 ise kaç tane farklı abc sıralı üçlüsü yazılabilir sorusu soruluyor.","Dersler düzenli takip eden ve yayınları takip eden herkesin eninde sonunda başarıya ulaşacağı belirtiliyor."]},"beginTime":535,"endTime":564,"href":"/video/preview/15305128301600373089?parent-reqid=1771672292170350-14258962204892842461-balancer-l7leveler-kubr-yp-sas-167-BAL&text=THATSAHAZARD10&t=535&ask_summarization=1"},{"index":5,"title":"Faktöriyel Problemleri","list":{"type":"unordered","items":["Z+ pozitif tam sayılar kümesinde, 9! içindeki 2, 3, 5 ve 7 asal sayılarının kuvvetlerinin toplamı 13'e eşittir.","19! = a × 10^b formunda yazıldığında, b'nin en büyük değeri 3'tür çünkü 19! içinde 3 tane 5 asal çarpanı vardır.","77! sayısının sondan 18 basamağı sıfırdır çünkü 77! içinde 18 tane 5 asal çarpanı vardır."]},"beginTime":2710,"endTime":3181,"href":"/video/preview/15305128301600373089?parent-reqid=1771672292170350-14258962204892842461-balancer-l7leveler-kubr-yp-sas-167-BAL&text=THATSAHAZARD10&t=2710&ask_summarization=1"},{"index":6,"title":"Permütasyon Kavramı","list":{"type":"unordered","items":["Permütasyon, bir kümenin elemanlarının seçilip sıralanması işlemidir.","n elemanlı bir kümenin r elemanlı her sıralı alt kümesine n'in r'li permütasyonu denir.","n'in r'li permütasyonu P(n,r) = n! / (n-r)! formülüyle hesaplanır."]},"beginTime":3181,"endTime":3303,"href":"/video/preview/15305128301600373089?parent-reqid=1771672292170350-14258962204892842461-balancer-l7leveler-kubr-yp-sas-167-BAL&text=THATSAHAZARD10&t=3181&ask_summarization=1"},{"index":7,"title":"Permütasyon Örnekleri","list":{"type":"unordered","items":["İkili permütasyon hesaplaması için faktöriyel formülü kullanılır: nPn = n! / (n-r)!, burada n=3 ve r=2 olduğunda 3! / (3-2)! = 6 bulunur.","Küçük sayılar için kolayca hesaplanabilirken, büyük sayılar için kısayol yöntemi kullanılabilir: nPn = n × (n-1) × ... × (n-r+1) formülü uygulanır.","Permütasyon problemlerinde faktöriyel ifadeleri temel alınır ve ardışık sayıların çarpımı kullanılarak çözümler bulunabilir."]},"beginTime":3307,"endTime":3412,"href":"/video/preview/15305128301600373089?parent-reqid=1771672292170350-14258962204892842461-balancer-l7leveler-kubr-yp-sas-167-BAL&text=THATSAHAZARD10&t=3307&ask_summarization=1"},{"index":8,"title":"Kitap Kullanımı ve Fen Lisesi İçeriği","list":{"type":"unordered","items":["Konuşmacı, sayfanın tamamının yazılı sorusu olduğunu belirtiyor ve öğrencilerden yazılı soruları WhatsApp üzerinden paylaşmalarını istiyor.","Kitapta Fen Lisesi kısmı da bulunuyor ve her öğrenci için uygun içerikler içeriyor.","Kitap, öğrencileri orta seviyeden başlayarak yukarı seviyeye taşımak için tasarlanmış."]},"beginTime":3414,"endTime":3505,"href":"/video/preview/15305128301600373089?parent-reqid=1771672292170350-14258962204892842461-balancer-l7leveler-kubr-yp-sas-167-BAL&text=THATSAHAZARD10&t=3414&ask_summarization=1"},{"index":9,"title":"Permütasyon Problemleri","list":{"type":"unordered","items":["İlk permütasyon problemi için P(n,2) = 11P(1) + 3 + 12 denklemi çözülüyor ve n = 7 olarak bulunuyor.","İkinci permütasyon problemi için 3P(n,2) = 6P(n-1,2) denklemi çözülüyor ve n = 4 olarak bulunuyor.","Yazılı soruları, öğrencilerin öğrenme seviyesini anlamak için daha zor seviyede hazırlanıyor."]},"beginTime":3505,"endTime":3595,"href":"/video/preview/15305128301600373089?parent-reqid=1771672292170350-14258962204892842461-balancer-l7leveler-kubr-yp-sas-167-BAL&text=THATSAHAZARD10&t=3505&ask_summarization=1"},{"index":10,"title":"Kitap Dizilimi Problemi","list":{"type":"unordered","items":["Altı farklı fizik, beş farklı matematik ve üç farklı kimya kitabı bir rafa dizilmesi isteniyor.","Ayni tür kitaplar bir arada olmak koşuluyla dizilim sayısı 3! × 5! × 3! × 6! olarak hesaplanıyor.","Başta ve sonda matematik kitabı olmak koşuluyla dizilim sayısı 5 × 4 × 12! olarak bulunuyor."]},"beginTime":3595,"endTime":3755,"href":"/video/preview/15305128301600373089?parent-reqid=1771672292170350-14258962204892842461-balancer-l7leveler-kubr-yp-sas-167-BAL&text=THATSAHAZARD10&t=3595&ask_summarization=1"},{"index":11,"title":"Öğrenci Sıralama Problemi","list":{"type":"unordered","items":["Beş kız ve dört erkek öğrenci, erkekler yan yana olmamak koşuluyla sıralanması isteniyor.","Önce kız öğrenciler 5! şekilde diziliyor ve aralarındaki boşluklara erkek öğrenciler yerleştiriliyor.","Toplam dizilim sayısı 5! × 6 × 5 × 4 × 3 = 5! × 360 olarak hesaplanıyor."]},"beginTime":3755,"endTime":3865,"href":"/video/preview/15305128301600373089?parent-reqid=1771672292170350-14258962204892842461-balancer-l7leveler-kubr-yp-sas-167-BAL&text=THATSAHAZARD10&t=3755&ask_summarization=1"},{"index":12,"title":"Kelime Dizilimi Problemi","list":{"type":"unordered","items":["\"Tonguç\" kelimesindeki harfler kullanılarak yazılabilecek tüm altı harfli kelimelerde u harfinin t harfinin solunda olma durumu inceleniyor.","Toplam 720 kelime yazılabilir ve bunların 360'sında u harfi t'nin solunda olur.","Ç harfinin n ve o harfleri arasında olma durumu için 240 kelime bulunuyor."]},"beginTime":3865,"endTime":4088,"href":"/video/preview/15305128301600373089?parent-reqid=1771672292170350-14258962204892842461-balancer-l7leveler-kubr-yp-sas-167-BAL&text=THATSAHAZARD10&t=3865&ask_summarization=1"},{"index":13,"title":"Aile Fotoğrafı Problemi","list":{"type":"unordered","items":["Anne, baba ve üç çocuktan oluşan bir aile, ortanca çocuk anne ve babanın arasında olmak koşuluyla fotoğraf çektirmek istiyor.","Anne, baba ve ortanca çocuk bir birim olarak düşünülerek 3! şekilde sıralanabilir.","Anne ve baba yerlerini değiştirerek toplam 3! × 2 = 2 × 6 = 12 farklı şekilde fotoğraf çektirebilirler."]},"beginTime":4088,"endTime":4155,"href":"/video/preview/15305128301600373089?parent-reqid=1771672292170350-14258962204892842461-balancer-l7leveler-kubr-yp-sas-167-BAL&text=THATSAHAZARD10&t=4088&ask_summarization=1"},{"index":14,"title":"Tekrarlı Permütasyon Formülü","list":{"type":"unordered","items":["Tekrarlı permütasyon formülü: n faktöriyel bölü n1 faktöriyel × n2 faktöriyel × ... × nk faktöriyel şeklinde hesaplanır.","Tekrarlı permütasyonda aynı elemanların yer değiştirmesi sonucu değişmediği için bölme işlemi yapılır.","Örneğin, aynı renkli kalemlerin yer değiştirmesi, toplam sıralamayı değiştirmez."]},"beginTime":4192,"endTime":4268,"href":"/video/preview/15305128301600373089?parent-reqid=1771672292170350-14258962204892842461-balancer-l7leveler-kubr-yp-sas-167-BAL&text=THATSAHAZARD10&t=4192&ask_summarization=1"},{"index":15,"title":"Tekrarlı Permütasyon Örnekleri","list":{"type":"unordered","items":["\"Karakura\" kelimesindeki harflerle anlamlı veya anlamsız sekiz harfli farklı kelimelerin sayısı: 8! / (2! × 3! × 2!)","11222333 sayısının rakamları ile yedi basamaklı farklı sayıların sayısı: 7! / (2! × 3! × 2!)","6 fizik, 5 matematik, 3 kimya kitabı ders türleri fark etmeksizin sıralanması: 14! / (4! × 5! × 3! × 6!)"]},"beginTime":4268,"endTime":4483,"href":"/video/preview/15305128301600373089?parent-reqid=1771672292170350-14258962204892842461-balancer-l7leveler-kubr-yp-sas-167-BAL&text=THATSAHAZARD10&t=4268&ask_summarization=1"},{"index":16,"title":"Sıfır İle Başlayan Sayılar","list":{"type":"unordered","items":["55,66 sayısının rakamları ile yedi basamaklı farklı sayıların sayısı hesaplanırken, sıfır ile başlayamama durumu dikkate alınmalıdır.","Önce sıfır olmayan rakamların yerleştirilmesi için 6! çarpma işlemi yapılır.","Sonra tekrarlı permütasyon formülü uygulanır: 6! / (2! × 2! × 3!)"]},"beginTime":4483,"endTime":4564,"href":"/video/preview/15305128301600373089?parent-reqid=1771672292170350-14258962204892842461-balancer-l7leveler-kubr-yp-sas-167-BAL&text=THATSAHAZARD10&t=4483&ask_summarization=1"},{"index":17,"title":"Altı Özdeş Oyuncak Sorunu","list":{"type":"unordered","items":["Altı özdeş oyuncak üç çocuğa kaç farklı şekilde dağıtılabilir sorusunda, özdeş oyuncakların farklı dağıtılsa da sonuç değişmeyeceği için tekrarlı permütasyon problemi oluşur.","Oyuncaklar bir çocuğa tamamı verilebilir veya farklı sayıda çocuklara dağıtılabilir.","Çözüm için 8 faktöriyel bölü 2 faktöriyel çarpı 6 faktöriyel formülü kullanılır."]},"beginTime":4620,"endTime":4717,"href":"/video/preview/15305128301600373089?parent-reqid=1771672292170350-14258962204892842461-balancer-l7leveler-kubr-yp-sas-167-BAL&text=THATSAHAZARD10&t=4620&ask_summarization=1"},{"index":18,"title":"Selim Kelimesi Sorusu","list":{"type":"unordered","items":["S harfinden başlayıp komşu harfleri takip ederek \"selim\" kelimesi kaç farklı şekilde oluşturulur sorusunda, dört adımda m'ye ulaşılabilmesi dört faktöriyel anlamına gelir.","Yatayda ve düşeyde iki adım olduğu için iki faktöriyel çarpı iki faktöriyel ile bölünür.","Sonuç olarak 4!/(2!×2!) = 24/4 = 6 farklı şekilde \"selim\" kelimesi oluşturulabilir."]},"beginTime":4717,"endTime":4822,"href":"/video/preview/15305128301600373089?parent-reqid=1771672292170350-14258962204892842461-balancer-l7leveler-kubr-yp-sas-167-BAL&text=THATSAHAZARD10&t=4717&ask_summarization=1"},{"index":19,"title":"Şehir Çizgileri Sorusu","list":{"type":"unordered","items":["Bir şehrin birbirini kesen caddelerinde A'dan C'ye, B'den C'ye, A'dan B'ye ve A'dan B'ye uğrayarak C'ye kaç farklı şekilde gidilebileceği sorulur.","A'dan C'ye gitmek için 10 faktöriyel bölü 6 faktöriyel çarpı 4 faktöriyel şeklinde çözülür.","B'den C'ye gitmek için 4 faktöriyel bölü 2 faktöriyel çarpı 2 faktöriyel şeklinde çözülür ve sonuç 6 farklı yoldur.","A'dan B'ye gitmek için 6 faktöriyel bölü 4 faktöriyel çarpı 2 faktöriyel şeklinde çözülür ve sonuç 15 farklı yoldur.","A'dan B'ye uğrayarak C'ye gitmek için A'dan B'ye olan 15 farklı yol ile B'den C'ye olan 6 farklı yol çarpılarak 90 farklı yol bulunur.","Alternatif olarak, her bir noktada önceki noktaların yol sayısının toplamı alınarak da çözüm 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