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I gave a short summary, and then we solved problems from Acil Publications' Permutation, Combination, and Probability Fascicle. I'll be uploading the second video to the channel tomorrow...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3579199/0113cc0d43f38db6df9b6433d7e65643/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/y7xwOQIAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"5","reqid":"1766823898031981-9801577751770958432-balancer-l7leveler-kubr-yp-sas-72-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1766823898031981-9801577751770958432-balancer-l7leveler-kubr-yp-sas-72-BAL&text=videoid:16950019177916090282","teaser":[{"list":{"type":"unordered","items":["Bu video, İbrahim Hoca tarafından sunulan bir matematik eğitim içeriğidir. Hoca, Acil Yayınları'nın fermantasyon, kombinasyon, binom ve olasılık kitabından permütasyon konusunu ele almaktadır.","Videoda permütasyon konusu detaylı olarak anlatılmakta ve çeşitli örnek sorular çözülmektedir. İlk olarak permütasyonun tanımı (n tane elemanın r'li sıralaması) ve faktöriyel kavramı kullanılarak permütasyon formülü (P(n,r) = n! / (n-r)!) açıklanmaktadır. Ardından dört öğrenci yedi koltuğa oturma, çift sayılarla palindron sayı oluşturma, masada kişilerin oturma düzeni ve evli çiftlerin eşler yan yana olmak şartıyla sıralanması gibi çeşitli permütasyon problemleri adım adım çözülmektedir.","Video, AYT sınavına hazırlanan öğrenciler için temel permütasyon sorularının çözüm tekniklerini göstermekte ve günlük hayattan örneklerle konuyu pekiştirmektedir. Hoca, özellikle masanın şekli ve deseni gibi detaylara dikkat edilmesi gerektiğini vurgulamakta ve soru çözüm mantığına odaklanmanın önemini anlatmaktadır."]},"endTime":1439,"title":"Permütasyon Konusu Eğitim Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"Soru Çözümü Serisi Tanıtımı","list":{"type":"unordered","items":["Acil Yayınları'nın fermantasyon, kombinasyon, binom ve olasılık kitabından soru çözümleri yapılacak.","Kitap konu anlatımlı olup, test kısmında zorlanılmayacağı belirtiliyor.","Videolar permütasyon, tekrarlı permütasyon, kombinasyon, binom ve olasılık konularını içerecek."]},"beginTime":11,"endTime":106,"href":"/video/preview/16950019177916090282?parent-reqid=1766823898031981-9801577751770958432-balancer-l7leveler-kubr-yp-sas-72-BAL&text=The+Solutions+-+Topic&t=11&ask_summarization=1"},{"index":1,"title":"Permütasyon Kavramı","list":{"type":"unordered","items":["Permütasyon, n ve r doğal sayıları için n ≥ r olmak üzere n elemanın r'li sıralamasıdır.","n'in r'li permütasyonu P(n,r) = n! / (n-r)! formülüyle hesaplanır.","Permütasyon, bir kümeyi belirli bir sırada düzenlemeyi ifade eder."]},"beginTime":106,"endTime":216,"href":"/video/preview/16950019177916090282?parent-reqid=1766823898031981-9801577751770958432-balancer-l7leveler-kubr-yp-sas-72-BAL&text=The+Solutions+-+Topic&t=106&ask_summarization=1"},{"index":2,"title":"Permütasyon Örnekleri","list":{"type":"unordered","items":["Dört öğrenci yan yana duran yedi koltuğa kaç farklı şekilde oturabilir sorusu çözülerek permütasyon kavramı açıklanıyor.","Aynı konsepte sahip elemanlar varsa, bunları bir bütün olarak düşünebiliriz.","Matematik kitapları bir arada olacak şekilde sıralama örneği veriliyor."]},"beginTime":216,"endTime":552,"href":"/video/preview/16950019177916090282?parent-reqid=1766823898031981-9801577751770958432-balancer-l7leveler-kubr-yp-sas-72-BAL&text=The+Solutions+-+Topic&t=216&ask_summarization=1"},{"index":3,"title":"Soru Çözümüne Başlangıç","list":{"type":"unordered","items":["Palindrom sayılar (soldan sağa ve sağdan sola aynı şekilde okunan sayılar) tanıtılıyor.","Beş basamaklı bir palindrom sayı örneği veriliyor.","A kümesindeki elemanlarla kaç tane çift sayı yazılabilmesi sorusu çözülecek."]},"beginTime":552,"endTime":583,"href":"/video/preview/16950019177916090282?parent-reqid=1766823898031981-9801577751770958432-balancer-l7leveler-kubr-yp-sas-72-BAL&text=The+Solutions+-+Topic&t=552&ask_summarization=1"},{"index":4,"title":"Çift ve Palindrom Sayı Sorusu","list":{"type":"unordered","items":["Çift sayı aranan bir soruda, son basamağa 2 veya 4 yazılabilir, bu nedenle 2 farklı seçenek vardır.","Palindrom sayı olması için ortadaki basamak mecburen 1 olmalıdır.","Geriye kalan basamaklara herhangi bir rakam konulabilir, bu durumda 6 farklı seçenek vardır.","Toplam durum sayısı 6 x 6 = 36 olup, çift sayı olma durumu için 2 farklı seçenek olduğu için toplam 72 durum vardır."]},"beginTime":586,"endTime":787,"href":"/video/preview/16950019177916090282?parent-reqid=1766823898031981-9801577751770958432-balancer-l7leveler-kubr-yp-sas-72-BAL&text=The+Solutions+-+Topic&t=586&ask_summarization=1"},{"index":5,"title":"Masa Oturma Sorusu","list":{"type":"unordered","items":["Mert ve Canan'ın karşı karşıya oturacağı şekilde 6 kişinin oturma durumları inceleniyor.","Mert ve Canan'ın oturabileceği 3 farklı yer vardır ve her yerde karşılıklı oturabilirler.","Geriye kalan 4 kişinin oturabileceği 4! = 24 farklı şekilde olabilir.","Toplam durum sayısı 3 x 2 x 24 = 144 olarak hesaplanır."]},"beginTime":787,"endTime":896,"href":"/video/preview/16950019177916090282?parent-reqid=1766823898031981-9801577751770958432-balancer-l7leveler-kubr-yp-sas-72-BAL&text=The+Solutions+-+Topic&t=787&ask_summarization=1"},{"index":6,"title":"Olasılık ve Permütasyon Sorularında Dikkat Edilmesi Gerekenler","list":{"type":"unordered","items":["Masanın şekli veya üzerindeki desen, permütasyon sorularında önemli bir faktör olabilir.","Sorularda görülen gereksiz detaylar atlanmamalı, sonradan onların etkisi değerlendirilmelidir.","Olasılık ve permütasyon sorularında çözüm mantığına odaklanmak, soru kalıplarına değil, daha fazla şey öğrenmeye yardımcı olur."]},"beginTime":896,"endTime":1009,"href":"/video/preview/16950019177916090282?parent-reqid=1766823898031981-9801577751770958432-balancer-l7leveler-kubr-yp-sas-72-BAL&text=The+Solutions+-+Topic&t=896&ask_summarization=1"},{"index":7,"title":"Çocukların Sıralanması Problemi","list":{"type":"unordered","items":["Dokuz çocuğun sıralanma problemi ele alınıyor, bu çocuklardan üçü kardeş.","Satır şeklinde sıralama yaparken, ilk çocuk 9 farklı şekilde, ikinci çocuk 6 farklı şekilde, üçüncü çocuk 3 farklı şekilde yerleştirilebilir.","Satır ve sütun şeklinde yapılan hesaplamalar aynı sonuç verir: 6 üzeri 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İçerikte asal sayıların tanımı ve özellikleri, aralarında asallık kavramı, asal çarpanlar, tam bölenler ve bunların sayıları gibi konular örneklerle açıklanmaktadır. Video, KPSS sınavına hazırlanan öğrenciler için hazırlanmış sorular üzerinden ilerlemekte ve her soru için detaylı çözüm yöntemleri sunulmaktadır.","Videoda ayrıca x+y=5 ve 2x-y=5 gibi denklemlerin çözümü, faktöriyel içindeki asal çarpanları tespit etme, pozitif tam bölen sayısı belirli olan sayıları bulma ve asal olmayan tam bölenlerin toplamı gibi konular da ele alınmaktadır. Video, sayı basamakları konusunun bir sonraki videoda ele alınacağı bilgisiyle sonlanmaktadır."]},"endTime":2554,"title":"KPSS Matematik: Asal Sayılar ve Bölenler Eğitim Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"Asal Sayılar Konusuna Giriş","list":{"type":"unordered","items":["Asal sayılar testi sekiz ile devam ediliyor ve bu konu çözdüğünüz tüm matematik konularıyla ilgilidir.","Asal sayılar, matematikte yapı taşı niteliğindedir ve tüm pozitif tam sayılar asal sayıların çarpımları şeklinde ifade edilebilir.","En küçük asal sayı iki'dir ve çift tek asal sayıdır; diğer asal sayılar üç, beş, yedi, onbir, onüç gibi tek sayılardır."]},"beginTime":0,"endTime":121,"href":"/video/preview/17965567997694286089?parent-reqid=1766823898031981-9801577751770958432-balancer-l7leveler-kubr-yp-sas-72-BAL&text=The+Solutions+-+Topic&t=0&ask_summarization=1"},{"index":1,"title":"Pozitif Tam Bölen Sayısı","list":{"type":"unordered","items":["Bir sayının pozitif tam bölenlerinin sayısını 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bulunabilir."]},"beginTime":283,"endTime":355,"href":"/video/preview/17965567997694286089?parent-reqid=1766823898031981-9801577751770958432-balancer-l7leveler-kubr-yp-sas-72-BAL&text=The+Solutions+-+Topic&t=283&ask_summarization=1"},{"index":3,"title":"Asal Sayılar ve Doğal Sayılar","list":{"type":"unordered","items":["Asal sayılar, iki sayının çarpımı şeklinde sadece kendisi çarpı bir veya eksi bir çarpı eksi asal sayı şeklinde yazılabilir.","İki doğal sayının çarpımı bir asal sayı olabilmesi için mutlaka bir çarpanının bir olması gerekir.","Soruda x ve y doğal sayıları için x+y=5 ve 2x-y=1 denklemleri çözülerek x=2 ve y=3 bulunur, çarpımları 6'dır."]},"beginTime":357,"endTime":508,"href":"/video/preview/17965567997694286089?parent-reqid=1766823898031981-9801577751770958432-balancer-l7leveler-kubr-yp-sas-72-BAL&text=The+Solutions+-+Topic&t=357&ask_summarization=1"},{"index":4,"title":"Aralarında Asal Sayılar","list":{"type":"unordered","items":["Aralarında asal sayılar, en büyük ortak bölenlerinin (EBOB) 1 olduğu sayılardır.","İki sayı aralarında asal olmak için ortak bölenleri olmamalıdır, örneğin 7 ve 15 aralarında asaldır çünkü ortak bölenleri yoktur."]},"beginTime":508,"endTime":590,"href":"/video/preview/17965567997694286089?parent-reqid=1766823898031981-9801577751770958432-balancer-l7leveler-kubr-yp-sas-72-BAL&text=The+Solutions+-+Topic&t=508&ask_summarization=1"},{"index":5,"title":"Asal Sayılar ve Özellikleri","list":{"type":"unordered","items":["Asal sayılar konusunda pozitiflik ve çiftlik teknikleri kullanılır.","Bir sayının basamaklarının toplamı 3'ün bir katıysa, o sayı 3'e bölünür ve asal değildir.","Tek bir sayının karesi tektir, çift bir sayının asal olması sadece 2 olduğu durumda mümkündür."]},"beginTime":597,"endTime":652,"href":"/video/preview/17965567997694286089?parent-reqid=1766823898031981-9801577751770958432-balancer-l7leveler-kubr-yp-sas-72-BAL&text=The+Solutions+-+Topic&t=597&ask_summarization=1"},{"index":6,"title":"Asal Sayı Problemleri","list":{"type":"unordered","items":["Çift sayılar (2 hariç) asal değildir çünkü mutlaka 2'ye bölünür.","83 sayısı asal sayıdır çünkü 3 üzeri 4 ile 2'nin toplamı 83'tür.","91 sayısı asal değildir çünkü 7 ile 13'ün çarpımıdır."]},"beginTime":652,"endTime":753,"href":"/video/preview/17965567997694286089?parent-reqid=1766823898031981-9801577751770958432-balancer-l7leveler-kubr-yp-sas-72-BAL&text=The+Solutions+-+Topic&t=652&ask_summarization=1"},{"index":7,"title":"Asal Sayılarla İlgili Bir Problemin Çözümü","list":{"type":"unordered","items":["x, y, z asal sayılar ve x=7y şeklinde verilmişse, y'nin 1 olması gerekir.","x=7, y=1 ve z=1 olarak bulunur.","a+b+c=7 olarak hesaplanır."]},"beginTime":753,"endTime":842,"href":"/video/preview/17965567997694286089?parent-reqid=1766823898031981-9801577751770958432-balancer-l7leveler-kubr-yp-sas-72-BAL&text=The+Solutions+-+Topic&t=753&ask_summarization=1"},{"index":8,"title":"Aralarında Asal Sayılar","list":{"type":"unordered","items":["Aralarında asal sayılarla ilgili problemlerde, verilen terimler üzerine oynamak gerekir.","Aralarında asal sayılarla ilgili problemlerde katlarla uğraşmamak ve bunları sindirmeye çalışmak önemlidir.","Aralarında asal sayılarla ilgili problemlerde, verilen sayıların katları olabilir ve bunları bulmak çözümü kolaylaştırır."]},"beginTime":842,"endTime":1065,"href":"/video/preview/17965567997694286089?parent-reqid=1766823898031981-9801577751770958432-balancer-l7leveler-kubr-yp-sas-72-BAL&text=The+Solutions+-+Topic&t=842&ask_summarization=1"},{"index":9,"title":"Sayıların Asal Çarpanlarına Ayrılması ve Tam Kare Yapılması","list":{"type":"unordered","items":["Sayıları asal çarpanlarına ayırarak sürekli yapı taşlarını indirerek yazabiliriz.","Bir sayıyı tam kare yapmak için, asal çarpanlarının kuvvetleri iki'nin katı olmalıdır.","Örneğin, 12 sayısını tam kare yapmak için 3 ile çarpabiliriz çünkü 2²×3×3=36, 6²'nin tam karesidir."]},"beginTime":1066,"endTime":1265,"href":"/video/preview/17965567997694286089?parent-reqid=1766823898031981-9801577751770958432-balancer-l7leveler-kubr-yp-sas-72-BAL&text=The+Solutions+-+Topic&t=1066&ask_summarization=1"},{"index":10,"title":"Sayıların Küp Olarak Yazılması","list":{"type":"unordered","items":["Bir sayının küpü olabilmesi için asal çarpanlarının kuvvetleri 3 ve 3'ün katı olmalıdır.","160 sayısını asal çarpanlarına ayırarak 2⁶×5³ şeklinde yazabiliriz ve bunu (2²×5)³ şeklinde yazarak b'nin küpüne eşitleyebiliriz.","a=50 ve b=20 olduğunda, a+b toplamı 70'dir."]},"beginTime":1265,"endTime":1416,"href":"/video/preview/17965567997694286089?parent-reqid=1766823898031981-9801577751770958432-balancer-l7leveler-kubr-yp-sas-72-BAL&text=The+Solutions+-+Topic&t=1265&ask_summarization=1"},{"index":11,"title":"Tam Bölen Sayıları Hesaplama","list":{"type":"unordered","items":["Bir sayının asal olmayan tam bölenlerinin sayısını hesaplamak için, önce tüm bölenlerin sayısını bulmak gerekir.","5ˣ×80 sayısının asal olmayan tam bölenleri 118 ise, tüm bölenlerin sayısı 120'dir ve pozitif tam bölen sayısı 60'dır.","Pozitif tam bölen sayısı formülü kullanılarak x=9 olarak bulunur."]},"beginTime":1416,"endTime":1577,"href":"/video/preview/17965567997694286089?parent-reqid=1766823898031981-9801577751770958432-balancer-l7leveler-kubr-yp-sas-72-BAL&text=The+Solutions+-+Topic&t=1416&ask_summarization=1"},{"index":12,"title":"Sayıların Pozitif Tam Bölenleri","list":{"type":"unordered","items":["Bin sayısını 2³ × 5³ şeklinde yazabiliriz.","Bir sayının pozitif tam bölen sayısını bulmak için, sayının asal çarpanlarının üslerine 1 ekleyip bunları çarparız.","2ⁿ⁻¹ × 5ⁿ⁻¹ şeklindeki bir sayının pozitif tam bölen sayısı 132 ise, n=11 olarak bulunur."]},"beginTime":1578,"endTime":1731,"href":"/video/preview/17965567997694286089?parent-reqid=1766823898031981-9801577751770958432-balancer-l7leveler-kubr-yp-sas-72-BAL&text=The+Solutions+-+Topic&t=1578&ask_summarization=1"},{"index":13,"title":"Faktöriyel ve Asal Çarpanlar","list":{"type":"unordered","items":["2ᵃ⁻¹ × n = 6! × 64 ve 3ᵇ⁺¹ × m = 7! × 81 şeklindeki denklemler çözülürken, faktöriyel içindeki asal çarpanların sayısını bulmak gerekir.","6! içinde 2'nin 4 kez, 7! içinde 3'ün 2 kez bulunduğu hesaplanır.","a=11 ve b=5 olarak bulunur, dolayısıyla a+b=16 olur."]},"beginTime":1731,"endTime":1940,"href":"/video/preview/17965567997694286089?parent-reqid=1766823898031981-9801577751770958432-balancer-l7leveler-kubr-yp-sas-72-BAL&text=The+Solutions+-+Topic&t=1731&ask_summarization=1"},{"index":14,"title":"Pozitif Tam Bölen Sayısı Üzerine","list":{"type":"unordered","items":["Üç basamaklı pozitif tam bölen sayısı 3 olan en küçük doğal sayı 121'dir (11²).","121'in pozitif tam bölenleri 1, 11 ve 121'dir.","120'in pozitif tam bölen sayısı 16'dır."]},"beginTime":1940,"endTime":2127,"href":"/video/preview/17965567997694286089?parent-reqid=1766823898031981-9801577751770958432-balancer-l7leveler-kubr-yp-sas-72-BAL&text=The+Solutions+-+Topic&t=1940&ask_summarization=1"},{"index":15,"title":"Asal Olmayan Tam Bölenlerin Toplamı","list":{"type":"unordered","items":["Asal olmayan tam bölenlerinin toplamı eksi onsekiz olacak şekilde sayılar inceleniyor.","77 sayısı (7×11) ve 7170 sayısı gibi, asal olmayan tam bölenlerinin toplamı eksi onsekiz olan örnekler veriliyor.","60, 72 ve 120 sayıları bu koşulu sağlamadığı için geçersiz bulunuyor."]},"beginTime":2135,"endTime":2254,"href":"/video/preview/17965567997694286089?parent-reqid=1766823898031981-9801577751770958432-balancer-l7leveler-kubr-yp-sas-72-BAL&text=The+Solutions+-+Topic&t=2135&ask_summarization=1"},{"index":16,"title":"Asal Çarpanların Toplamının Yarısı","list":{"type":"unordered","items":["Bir sayının birbirinden farklı asal çarpanlarının toplamının yarısı 15 ise, bu sayı 3 ve 5'in çarpımı şeklinde olmalı.","Asal çarpanların toplamının yarısı 6 olan en küçük iki doğal sayı 35 (5×7) ve 42 (2×3×7) olarak bulunuyor.","Asal çarpanların toplamı 12 olacak şekilde iki, üç, beş ve yedi asal sayıları kombinasyonuyla çözüm bulunuyor."]},"beginTime":2254,"endTime":2402,"href":"/video/preview/17965567997694286089?parent-reqid=1766823898031981-9801577751770958432-balancer-l7leveler-kubr-yp-sas-72-BAL&text=The+Solutions+-+Topic&t=2254&ask_summarization=1"},{"index":17,"title":"Asal Olmayan Tam Bölen Sayısı","list":{"type":"unordered","items":["320 sayısının asal olmayan tam bölen sayısı hesaplanıyor ve 26 olarak bulunuyor.","320 sayısının asal olmayan tam bölen sayısı 26 olduğundan, 26'dan küçük en büyük asal sayı 23 olarak belirleniyor.","Video sonunda Instagram adresleri paylaşılıyor ve diğer dosyaların Telegram üzerinden erişilebileceği 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