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Hoca, tekrarlı permütasyon konusunu anlatmaktadır.","Videoda tekrarlı permütasyon konusu detaylı olarak ele alınmaktadır. Hoca, tekrarlı permütasyonun ne olduğunu açıklayarak başlayıp, faktöriyel kullanarak çözüm yöntemlerini göstermektedir. Ders boyunca Messi kelimesi, rakamlarla ilgili bir sayı problemi, \"seyretti\" kelimesi, \"Kocaeli\" kelimesi, yol problemleri ve özdeş oyuncakların dağıtılması gibi çeşitli örnekler üzerinden tekrarlı permütasyon konusu pekiştirilmektedir. Her örnek için adım adım çözüm yöntemi gösterilmekte ve farklı çözüm teknikleri paylaşılmaktadır."]},"endTime":716,"title":"Tekrarlı Permütasyon Matematik Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Tekrarlı Permütasyon Kavramı","list":{"type":"unordered","items":["Tekrarlı permütasyon, permütasyonun alt gruplarından biridir ve içinde tekrar eden harfler veya sayılar olan gruplarda kullanılır.","Tekrarlı permütasyon hesaplanırken toplam adet faktöriyeline, tekrar eden adetlerin faktöriyelleri bölünür."]},"beginTime":1,"endTime":71,"href":"/video/preview/5066438695003469698?channelId=d3d3LnlvdXR1YmUuY29tO1VDZzdKT28yZE1LNkw2cTZqRWRqM2xmdw%3D%3D&how=tm&parent-reqid=1752787580987595-2589943177609086329-balancer-l7leveler-kubr-yp-vla-101-BAL&text=Deney+Akademi&t=1&ask_summarization=1"},{"index":1,"title":"Messi Kelimesi Örneği","list":{"type":"unordered","items":["Messi kelimesinin harfleriyle anlamlı veya anlamsız beş harfli kelimeler yazılabilir.","Messi kelimesinde tekrar eden harfler \"e\" olup iki tane olduğu için çözüm 5! / 2! şeklinde yapılır.","Sonuç olarak 60 farklı kelime yazılabileceği bulunur."]},"beginTime":71,"endTime":154,"href":"/video/preview/5066438695003469698?channelId=d3d3LnlvdXR1YmUuY29tO1VDZzdKT28yZE1LNkw2cTZqRWRqM2xmdw%3D%3D&how=tm&parent-reqid=1752787580987595-2589943177609086329-balancer-l7leveler-kubr-yp-vla-101-BAL&text=Deney+Akademi&t=71&ask_summarization=1"},{"index":2,"title":"Rakamlarla Tekrarlı Permütasyon","list":{"type":"unordered","items":["22237 rakamlarının yer değiştirilerek yedi basamaklı sayılar oluşturulması sorusunda, sıfırla başlamadığı için en büyük basamak 5 farklı rakamdan biri alabilir.","Çözüm 5! / (3! × 2! × 2!) şeklinde yapılır.","Sonuç olarak 150 farklı sayı oluşturulabileceği bulunur."]},"beginTime":154,"endTime":262,"href":"/video/preview/5066438695003469698?channelId=d3d3LnlvdXR1YmUuY29tO1VDZzdKT28yZE1LNkw2cTZqRWRqM2xmdw%3D%3D&how=tm&parent-reqid=1752787580987595-2589943177609086329-balancer-l7leveler-kubr-yp-vla-101-BAL&text=Deney+Akademi&t=154&ask_summarization=1"},{"index":3,"title":"Kelime Okuma Problemleri","list":{"type":"unordered","items":["\"Seyretti\" kelimesinin farklı okunuşları hesaplanırken, \"s\" harfi başlangıç harfi olarak karalanır.","Geriye kalan harfler 5! / (3! × 2!) şeklinde hesaplanır ve sonuç 10 farklı okunuş bulunur.","\"Kocaeli\" kelimesinin farklı okunuşları hesaplanırken, \"k\" harfi başlangıç harfi olarak karalanır ve sonuç 20 farklı okunuş bulunur."]},"beginTime":262,"endTime":443,"href":"/video/preview/5066438695003469698?channelId=d3d3LnlvdXR1YmUuY29tO1VDZzdKT28yZE1LNkw2cTZqRWRqM2xmdw%3D%3D&how=tm&parent-reqid=1752787580987595-2589943177609086329-balancer-l7leveler-kubr-yp-vla-101-BAL&text=Deney+Akademi&t=262&ask_summarization=1"},{"index":4,"title":"Yol Problemleri","list":{"type":"unordered","items":["A noktasından C noktasına B'ye uğramak şartıyla gidilebilecek yollar hesaplanırken, A-B ve B-C yolları ayrı ayrı hesaplanır.","A-B arası 5 farklı yol, B-C arası 3 farklı yol olduğu için toplam 10×3=30 farklı yol bulunur.","Alternatif olarak, A-B ve B-C yolları için ayrı ayrı sayılar bulunup çarpılarak da aynı sonuç elde edilebilir."]},"beginTime":443,"endTime":614,"href":"/video/preview/5066438695003469698?channelId=d3d3LnlvdXR1YmUuY29tO1VDZzdKT28yZE1LNkw2cTZqRWRqM2xmdw%3D%3D&how=tm&parent-reqid=1752787580987595-2589943177609086329-balancer-l7leveler-kubr-yp-vla-101-BAL&text=Deney+Akademi&t=443&ask_summarization=1"},{"index":5,"title":"Ayraç Yöntemi","list":{"type":"unordered","items":["Altı özdeş oyuncak üç çocuğa kaç farklı şekilde dağıtılabilir sorusunda ayraç yöntemi kullanılır.","Oyuncaklara x, çocuklara ayraçlar konularak toplam 8 eleman elde edilir.","Çözüm 8! 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Gazi Hoca, Altı Akademi'nde köklü sayılar konusunu anlatmaktadır.","Video, köklü sayıların temel kurallarını ve uygulamalarını içermektedir. İlk olarak tek ve çift kuvvetlerin kök dışına çıkarılması, mutlak değer kavramı ve karekökün anlamı açıklanmaktadır. Ardından tam kare sayıların kök dışına çıkarılması, üçlü ve dörtlü köklerin çözümü ve tam kare olmayan sayıların kök dışına çıkarılması yöntemleri örneklerle anlatılmaktadır. Video boyunca çeşitli örnekler çözülerek konu pekiştirilmektedir."]},"endTime":691,"title":"Köklü Sayılar Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Köklü Sayılar Kavramı","list":{"type":"unordered","items":["Köklü sayılar matematikte özellikle kök dışına çıkarma ve kök içindeki sayıyı oynatma konusunda zorluk yaratan bir konudur.","Köklü sayılar, bir sayının kuvvetinin kök derecesiyle bölünmesiyle elde edilir."]},"beginTime":0,"endTime":22,"href":"/video/preview/1087225278908735453?channelId=d3d3LnlvdXR1YmUuY29tO1VDZzdKT28yZE1LNkw2cTZqRWRqM2xmdw%3D%3D&how=tm&parent-reqid=1752787580987595-2589943177609086329-balancer-l7leveler-kubr-yp-vla-101-BAL&text=Deney+Akademi&t=0&ask_summarization=1"},{"index":1,"title":"Tek Kuvvetli Kökler","list":{"type":"unordered","items":["Bir x sayısının tek kuvveti tek dereceden kök alınmışsa, x işareti ile beraber dışarıya çıkar.","Örneğin, 7⁵√5 = 7 ve (-2)³√3 = -2 olarak hesaplanır."]},"beginTime":22,"endTime":72,"href":"/video/preview/1087225278908735453?channelId=d3d3LnlvdXR1YmUuY29tO1VDZzdKT28yZE1LNkw2cTZqRWRqM2xmdw%3D%3D&how=tm&parent-reqid=1752787580987595-2589943177609086329-balancer-l7leveler-kubr-yp-vla-101-BAL&text=Deney+Akademi&t=22&ask_summarization=1"},{"index":2,"title":"Çift Kuvvetli Kökler","list":{"type":"unordered","items":["Bir x sayısının çift kuvveti aynı çift kuvvetle kök alınmışsa, x sayısı dışarıya mutlak değer olarak çıkar.","Örneğin, 4²√2 = 4 ve (-3)⁴√4 = |-3| = 3 olarak hesaplanır."]},"beginTime":72,"endTime":204,"href":"/video/preview/1087225278908735453?channelId=d3d3LnlvdXR1YmUuY29tO1VDZzdKT28yZE1LNkw2cTZqRWRqM2xmdw%3D%3D&how=tm&parent-reqid=1752787580987595-2589943177609086329-balancer-l7leveler-kubr-yp-vla-101-BAL&text=Deney+Akademi&t=72&ask_summarization=1"},{"index":3,"title":"Karekök Kavramı","list":{"type":"unordered","items":["Karekök, bir x sayısının ikinci dereceden kök alınması demektir ve kök derecesi yazılmazsa 2 olarak kabul edilir.","Tam kare sayıların kök dışına çıkması kolaydır, örneğin √1 = 1, √25 = 5, √121 = 11 olarak hesaplanır."]},"beginTime":204,"endTime":311,"href":"/video/preview/1087225278908735453?channelId=d3d3LnlvdXR1YmUuY29tO1VDZzdKT28yZE1LNkw2cTZqRWRqM2xmdw%3D%3D&how=tm&parent-reqid=1752787580987595-2589943177609086329-balancer-l7leveler-kubr-yp-vla-101-BAL&text=Deney+Akademi&t=204&ask_summarization=1"},{"index":4,"title":"Çoklu Kökler","list":{"type":"unordered","items":["Üçlü veya dörtlü köklerde en içteki kökten başlanır ve içten dışa doğru işlem yapılır.","Örneğin, √(25-√9+√4) = √(5-5+2) = √2 = 2 olarak hesaplanır."]},"beginTime":311,"endTime":428,"href":"/video/preview/1087225278908735453?channelId=d3d3LnlvdXR1YmUuY29tO1VDZzdKT28yZE1LNkw2cTZqRWRqM2xmdw%3D%3D&how=tm&parent-reqid=1752787580987595-2589943177609086329-balancer-l7leveler-kubr-yp-vla-101-BAL&text=Deney+Akademi&t=311&ask_summarization=1"},{"index":5,"title":"Tam Kare Olmayan Sayıların Kökten Çıkması","list":{"type":"unordered","items":["Tam kare olmayan sayıların kökten çıkması için sayı asal çarpanlarına ayrılır ve kare olan kuvvetler dışarı çıkarılır.","Örneğin, √12 = √(2²×3) = 2√3, √50 = √(2×5²) = 5√2 olarak hesaplanır.","Büyük sayılar için asal çarpanlara ayırma yöntemi kullanılır, örneğin √150 = √(2×3²×5²) = 5√6 olarak hesaplanır."]},"beginTime":428,"endTime":687,"href":"/video/preview/1087225278908735453?channelId=d3d3LnlvdXR1YmUuY29tO1VDZzdKT28yZE1LNkw2cTZqRWRqM2xmdw%3D%3D&how=tm&parent-reqid=1752787580987595-2589943177609086329-balancer-l7leveler-kubr-yp-vla-101-BAL&text=Deney+Akademi&t=428&ask_summarization=1"}],"linkTemplate":"/video/preview/1087225278908735453?channelId=d3d3LnlvdXR1YmUuY29tO1VDZzdKT28yZE1LNkw2cTZqRWRqM2xmdw%3D%3D&how=tm&parent-reqid=1752787580987595-2589943177609086329-balancer-l7leveler-kubr-yp-vla-101-BAL&text=Deney+Akademi&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"11 DK'da Köklü Sayılar - 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