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Tüm bunların cevabını bu video 'da...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3106743/94396ca158a270e976b751c3c29f3655/564x318_1"},"target":"_self","position":"0","reqid":"1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL","summary":{"fullTextUrl":"/int_search_summary?data=http%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3Dl_u5nTF6FIE","linkTemplate":"/video/preview/16929307457405527952?parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=P.K&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Abdullah Öcalan P.K.K'yı Nasıl Kurdu - P.K.K Nedir Hedefi ve İdolojisi Nedir","related_orig_text":"P.K","related_porno":false,"related_less_3m_off":true,"client":"d2d","no_cnt":1,"related_src":"serp","related":"{\"porno\":false,\"vfp\":1,\"orig_text\":\"P.K\",\"url\":\"http:\\/\\/www.youtube.com\\/watch?v=l_u5nTF6FIE\",\"src\":\"serp\",\"rvb\":\"EqsDChQxNjkyOTMwNzQ1NzQwNTUyNzk1MgoSNDk2NzM2MTc5NjQ2NTIzMjM2ChQxNjI4Nzg5OTU4MjI1NjIwNTA4MQoUMTcyNTY4MTgwODQxNTE5NzkwNzMKEzI3MDQ5NjY5NTM2ODI4ODg3MjMKFDEyOTAxODAwMzM4OTg0MDk4NzUxChQxNTI2Mjc2NDIzMjA2MTMzODI5MQoTNjU2ODk3NjAzNzQ1MDI2OTEyNQoUMTIwNDEzNjE1MTkzNzIzMTA0MjEKEzgyMTUzNDcwODI5Nzg0MDA1MDYKFDE3NDMzNTcwNjkwNjM2NTE5NjgzChM1ODQ5MjM1NDQzNDg1Mzc2OTM2ChQxMjgwMjEyNDIyNjkwNTI5OTg4MQoSMTk4NDMwNjUwNTM1ODMyNzI4ChMzODAxMjc1MzE4NTMyMjg5MzY1ChM5OTA5NTY2Nzk1Mzg0OTgwMzY1ChM4NzY2MTM2MDA0NTQ4MzgwMjQ5ChM5NDg4NjYwNTYyNjc5ODE2MzkyChQxNTMyOTcyMTU4OTY2MzMzMjMwMAoTNjIzMTk1OTY5MjkxNTk1ODM4MBoWChQxNjkyOTMwNzQ1NzQwNTUyNzk1MloUMTY5MjkzMDc0NTc0MDU1Mjc5NTJqrQ0SATAYACJDGi8ACihoaGVnYm9kYXFteXBkcWhoVUNZeDJBME9GSnJRbXB3RGhWRDNUUnd3EgIAECoQwg8PGg8_E-cDggQkAYAEKyqLARABGniBAQACBv8CAPn--QQNBf0B-_wE_fn9_QDw-AgF9AEAAO0ECPIAAAAA_QL7BgEAAADw9_AH-wAAAAsBAP_sAP8AD_r89fYAAADvCvoC_wEAABQT-PkC_wAAEgoIAf8AAAAOCPQM_wAAAAL59vwAAAAA_-8HAQAAAAAgAC1etdg7OBNACUhOUAIqcxAAGmDXBABBNuMbvPgf5BwnMfH-2cT65cj5_x77AKYcCv0cG4uQIgsALvEV65sAAAA0BhIDNADzf9QXvxHPMzn1Rd4M-3lGCA_3R1XRIgES4O36Be8PPCUAGPq41jvelm8iMfcgAC3bJA47OBNACUhvUAIqrwYQDBqgBgAAUMIAAOBBAAAAQgAAYEEAAITCAAAAwgAAnEIAALTCAABAwAAAwMAAACxCAACAPwAA2MEAAIzCAAAYQgAAhsIAAIBBAABAwgAAwEAAABzCAADAQgAA4EAAAKBBAADoQQAAoEAAAHBBAAAAwAAAaMIAAABBAADgQQAADMIAACRCAABkwgAAQEIAAIA_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-AACCPgAAQDwAAMg9AAAwvQAAzr4AAEC8AACmPgAAgLsAABC9AACePgAAXD4AACQ-AACYvQAAmL0AAAQ-AAC2PgAAqj4AAH8_AACIvQAAPD4AAGS-AACOvgAAXL4AACQ-AABMvgAAgLsAAJI-AAAwPQAAqD0AAKi9AACgvAAAgDsAAFA9AABAPAAAyL0AALq-AADYvQAAfD4AAOi9AAC4PQAAQLwAAGw-AADYPQAAuL0AAES-AAD4vQAAvr4AABS-AAD4PQAA1j4AAKA8AADIvQAABD4AAA8_AACivgAAED0AABw-AACAOwAATL4AAKi9AACSviAAOBNACUh8UAEqjwIQARqAAgAAlr4AAOA8AACYvQAAO78AAPi9AACqPgAAJT8AAFw-AACWvgAA3j4AAFQ-AABEvgAAqL0AAEA8AABUvgAAyD0AABw-AABjPwAAuD0AABw-AACmPgAAQDwAAAw-AAA8PgAAVL4AAFQ-AACoPQAApj4AAII-AAAsvgAAqD0AAEy-AACKvgAAhr4AANi9AAC4vQAALD4AAN6-AABsvgAAZL4AAGQ-AAD4PQAAmj4AAMi9AAA8PgAA6j4AAH-_AAAQPQAAhj4AAJg9AABQvQAAwj4AAMi9AACCPgAAXD4AABQ-AAAQvQAAtj4AAMo-AABwvQAA-D0AAI6-AACgvAAAQDwgADgTQAlIfFABMAk4AUoAYABoAA,,\"}","related_url":"http://www.youtube.com/watch?v=l_u5nTF6FIE","parent-reqid":"1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL","related_vfp":1,"relatedVideo":"yes"},"cwidth":1280,"cheight":720,"cratio":1.77777,"dups":["16929307457405527952"],"episode":0,"season":0,"isEmbedOnly":false,"greenHost":"YouTube","hasTranslation":true,"contentTypeId":null,"censored":false,"censoredShock":false,"isShockDoc":false},"496736179646523236":{"videoId":"496736179646523236","docid":"34-6-8-Z0C9F779D46C4364B","description":"P.K. bi şehirdeki yabancının düşünceler komedisidir. 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AYT Matematik KONU - KAYA - ELİT TÜM Pdfler...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3281834/8daea5e067d30e9d7bd949eff494fba9/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/78_zPQIAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"8","reqid":"1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=videoid:15262764232061338291","teaser":[{"list":{"type":"unordered","items":["Bu video, Lapto Matematik YouTube kanalında Ek Hoca tarafından sunulan bir matematik eğitim içeriğidir. Video, permütasyon, kombinasyon, binom ve olasılık konularını kapsayan bir serinin ilk bölümüdür.","Video, üç bölümden oluşan bir serinin ilk kısmını oluşturmaktadır: konu anlatımı, eski nesil sorular ve yeni nesil sorular. İçerikte sayma kuralları, permütasyon, kombinasyon, binom, basit olayların olasılıkları ve koşullu olasılık konuları ele alınmaktadır. Eğitmen, teorik bilgileri örnek sorular üzerinden açıklamakta ve adım adım çözüm yöntemlerini göstermektedir.","Videoda faktöriyel kavramı, permütasyon formülü (P(n,r) = n! / (n-r)!), kombinasyon formülü ve özellikleri detaylı olarak anlatılmaktadır. Ayrıca farklı renkte eşyaların seçimi, nöbetçi öğretmenlerin dağılımı, kitapların sıralanması, harflerin yer değiştirilmesi gibi çeşitli problem türleri çözülmektedir. TYT sınavına hazırlanan öğrenciler için 10. sınıfa kadar olan konular, AYT sınavına hazırlananlar için ise koşullu olasılık konusu önemlidir."]},"endTime":16201,"title":"Permütasyon, Kombinasyon ve Olasılık Konu Anlatımı ve Problem Çözümleri","beginTime":0}],"fullResult":[{"index":0,"title":"Ders Serisi Tanıtımı","list":{"type":"unordered","items":["Bu video, permütasyon, kombinasyon, binom ve olasılık konularını içeren on beşinci bölümün ilk videosudur.","Toplam üç video olacak: ilk video konu anlatımı, ikinci video eski nesil sorular, üçüncü video yeni nesil sorular.","Konular olasılık kapsamında kullanılır ve TYT'de basit olayların olasılıkları, AYT'de koşullu olasılık konuları çıkmaktadır."]},"beginTime":6,"endTime":96,"href":"/video/preview/15262764232061338291?parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=P.K&t=6&ask_summarization=1"},{"index":1,"title":"Toplama Yoluyla Sayma","list":{"type":"unordered","items":["Toplama yoluyla sayma, sonlu ve ayrık kümelerin eleman sayılarının toplamının, bu kümelerin birleşimlerinin eleman sayısına eşit olduğu kavramdır.","Ayrık kümeler, kesişimleri boş olan iki farklı kümedir.","Örnek olarak, üç elma ve iki portakal arasından bir meyve seçme durumunda toplam 5 farklı seçenek vardır."]},"beginTime":96,"endTime":313,"href":"/video/preview/15262764232061338291?parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=P.K&t=96&ask_summarization=1"},{"index":2,"title":"Çarpma Yoluyla Sayma","list":{"type":"unordered","items":["Çarpma yoluyla sayma, kartezyen küme çarpımıdır ve A kümesinin eleman sayısı ile B kümesinin eleman sayısının çarpımıdır.","Örnek olarak, her birinde 5 kitap bulunan 14 farklı kitaplıkta toplam 70 kitap vardır (14 x 5 = 70).","Diğer bir örnek olarak, üç farklı çiçek beş öğretmene dağıtımı 60 farklı şekilde yapılabilir (5 x 4 x 3 = 60)."]},"beginTime":313,"endTime":479,"href":"/video/preview/15262764232061338291?parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=P.K&t=313&ask_summarization=1"},{"index":3,"title":"Farklı Renkte Şapka, Pantolon ve Ayakkabı Seçimi","list":{"type":"unordered","items":["Bir mağazada iki farklı renkte şapka, üç farklı renkte pantolon ve iki farklı renkte ayakkabı bulunmaktadır.","Hakkı her biri farklı renkte olacak şekilde bir şapka, bir pantolon ve bir ayakkabı seçmek istemektedir.","Dallanma yöntemi kullanılarak, Hakkı'nın bu seçimleri 8 farklı şekilde yapılabileceği bulunmuştur."]},"beginTime":486,"endTime":708,"href":"/video/preview/15262764232061338291?parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=P.K&t=486&ask_summarization=1"},{"index":4,"title":"Mektup ve Posta Kutusu Sorunu","list":{"type":"unordered","items":["Üç farklı mektup dört farklı posta kutusuna atılabilir.","Her posta kutusuna en fazla bir mektup atılabilir koşulu olmadan, mektuplar 64 farklı şekilde atılabilir.","Her posta kutusunda en çok bir mektup olmak koşuluyla, mektuplar 24 farklı şekilde atılabilir."]},"beginTime":708,"endTime":808,"href":"/video/preview/15262764232061338291?parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=P.K&t=708&ask_summarization=1"},{"index":5,"title":"Sesli Harf ve Rakam Sıralı İkili Sorunu","list":{"type":"unordered","items":["Bir sesli harf ve bir rakamdan oluşan sıralı ikililerin sayısı hesaplanmaktadır.","Sesli harf kümesinde 8 eleman, rakam kümesinde 10 eleman bulunmaktadır.","Kartezian çarpım yöntemiyle, toplam 80 farklı sıralı ikili oluşturulabilir."]},"beginTime":808,"endTime":871,"href":"/video/preview/15262764232061338291?parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=P.K&t=808&ask_summarization=1"},{"index":6,"title":"Şehirler Arası Yol Seçimi","list":{"type":"unordered","items":["A ile B arasında 5 farklı yol, B ile C arasında 3 farklı yol bulunmaktadır.","A'dan C'ye gidilmesi için 15 farklı yol bulunmaktadır.","A'dan C'ye gidip tekrar A'ya dönülmesi için 225 farklı yol bulunmaktadır.","Giderken kullanılan yollar dönerken kullanılmaması koşuluyla, A'dan C'ye gidip A'ya geri dönülmesi için 120 farklı yol bulunmaktadır."]},"beginTime":871,"endTime":988,"href":"/video/preview/15262764232061338291?parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=P.K&t=871&ask_summarization=1"},{"index":7,"title":"Nöbetçi Öğretmen Sorusu","list":{"type":"unordered","items":["Bir okulda altı nöbetçi öğretmenin bulunduğu bir günde beşinci ders saatinde dört sınıfın dersi boştur.","Derslerin boş geçmemesi için dersi boş olan sınıflara her birine bir nöbetçi öğretmen girecektir.","Nöbetçi öğretmenler bu sınıflara 360 farklı şekilde girebilir."]},"beginTime":1007,"endTime":1084,"href":"/video/preview/15262764232061338291?parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=P.K&t=1007&ask_summarization=1"},{"index":8,"title":"Üç Basamaklı Tek Sayılar","list":{"type":"unordered","items":["A kümesi {1, 2, 3, 4, 7, 9} elemanlarıyla üç basamaklı rakamları farklı tek doğal sayılar yazılabilir.","Sayının tek olması için son basamağı 1, 3, 7 veya 9 olmalıdır.","Toplam 80 farklı üç basamaklı tek sayı yazılabilir."]},"beginTime":1084,"endTime":1153,"href":"/video/preview/15262764232061338291?parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=P.K&t=1084&ask_summarization=1"},{"index":9,"title":"Üç Basamaklı Sayılar","list":{"type":"unordered","items":["A kümesi {1, 2, 3, 4, 5, 6} elemanlarıyla üç basamaklı farklı doğal sayılar yazılabilir.","Rakamları farklı olmasa da, toplam 216 farklı üç basamaklı sayı yazılabilir.","Bu sayıların yarısı, yani 108 farklı çift doğal sayı yazılabilir."]},"beginTime":1153,"endTime":1249,"href":"/video/preview/15262764232061338291?parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=P.K&t=1153&ask_summarization=1"},{"index":10,"title":"Belirli Aralıklarda Sayılar","list":{"type":"unordered","items":["A kümesi elemanlarıyla 200 ile 500 arasında 108 farklı doğal sayı yazılabilir.","240 ile 600 arasında 126 farklı tek doğal sayı yazılabilir.","Bu sonuç, 200 ile 600 arasında toplam sayıdan 240 ile 200 arasındaki sayıları çıkarıp, kalanın yarısını hesaplayarak bulunmuştur."]},"beginTime":1249,"endTime":1471,"href":"/video/preview/15262764232061338291?parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=P.K&t=1249&ask_summarization=1"},{"index":11,"title":"Beş Basamaklı Sayılar","list":{"type":"unordered","items":["A kümesi {1, 2, 3, 4} elemanlarıyla beş basamaklı rakamları farklı 600 doğal sayı yazılabilir.","Bu sayıların 312 tanesi çift doğal sayıdır.","Çift sayılar için sıfırın son basamakta olma ve olmama durumları ayrı ayrı hesaplanmıştır."]},"beginTime":1471,"endTime":1697,"href":"/video/preview/15262764232061338291?parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=P.K&t=1471&ask_summarization=1"},{"index":12,"title":"Faktöriyel Kavramı","list":{"type":"unordered","items":["Birbirinden farklı n tane nesne yan yana en faktöriyel şekilde sıralanabilir.","Örneğin üç kişi üç koltuğa otururken 3! (3 faktöriyel) farklı şekilde sıralanabilir.","Permütasyon, kombinasyon ve özellikle faktöriyel işlemleri bu tür sorularda çok fazla kullanılır."]},"beginTime":1697,"endTime":1737,"href":"/video/preview/15262764232061338291?parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=P.K&t=1697&ask_summarization=1"},{"index":13,"title":"Faktöriyel Kavramı","list":{"type":"unordered","items":["Faktörler konusunda eksik bilgiye sahip olanlar, temel kavramlar videosundan yararlanabilirler.","Karekodu okutarak veya \"temel kavramlar konu anlatımı\" yazarak faktörlere ulaşılabilir.","Altı kişi altı sandalye problemi, altı faktöriyel (720) şeklinde çözülebilir."]},"beginTime":1744,"endTime":1824,"href":"/video/preview/15262764232061338291?parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=P.K&t=1744&ask_summarization=1"},{"index":14,"title":"Permütasyon Örnekleri","list":{"type":"unordered","items":["Altı kişilik bir ailenin yan yana sıralanma sayısı, altı faktöriyel (720) şeklinde hesaplanır.","Anne ve baba bir arada olmak koşuluyla sıralama sayısı, beş faktöriyel çarpı iki faktöriyel (240) olarak bulunur.","Permütasyon, bir kümenin r'li elemanlarının sıralanmasıdır ve P(n,r) = n! / (n-r)! formülüyle hesaplanır."]},"beginTime":1824,"endTime":2006,"href":"/video/preview/15262764232061338291?parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=P.K&t=1824&ask_summarization=1"},{"index":15,"title":"Permütasyon Problemleri","list":{"type":"unordered","items":["Beş elemanlı bir kümenin ikili permütasyonları, P(5,2) = 5×4 = 20 şeklinde hesaplanır.","Bir kümenin dörtlü permütasyonları 840 olan kümenin eleman sayısı, 7 olarak bulunur.","Permütasyon (n+2,5) bölü permütasyon (n-1,3) = 105 olduğuna göre n = 5 olarak hesaplanır."]},"beginTime":2006,"endTime":2268,"href":"/video/preview/15262764232061338291?parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=P.K&t=2006&ask_summarization=1"},{"index":16,"title":"Kombinasyon ve Permütasyon Farkı","list":{"type":"unordered","items":["Kümelerde alt küme sayısı hesaplanırken kombinasyon kullanılır, permütasyon ise sıralama için kullanılır.","Kombinasyonda elemanların sıralaması önemli değildir, permütasyonda ise önemlidir.","Kümelerde alt küme sayısı hesaplanırken kombinasyon formülü kullanılır, permütasyonda ise faktöriyel formülü kullanılır."]},"beginTime":2268,"endTime":2367,"href":"/video/preview/15262764232061338291?parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=P.K&t=2268&ask_summarization=1"},{"index":17,"title":"Permütasyon Problemleri","list":{"type":"unordered","items":["a, b, c, d, f, g kümesinin üçlü permütasyonlarında b elemanı bulunanların sayısı, yedi elemanlı kümenin üçlü permütasyonları (7×6×5=210) ile b'nin bulunmadığı altı elemanlı kümenin üçlü permütasyonları (6×5×4=120) arasındaki fark olarak hesaplanır (210-120=90).","Üçlü permütasyonlar ile üç elemanlı alt kümeler aynı şey değildir; üçlü permütasyon derse permütasyon yapılırken, üç elemanlı alt küme derse kombinasyon yapılır.","LAPT kümesinin üçlü permütasyonlarında L elemanı bulunurken F elemanı bulunmayacak şekilde 18 farklı permütasyon vardır."]},"beginTime":2369,"endTime":2590,"href":"/video/preview/15262764232061338291?parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=P.K&t=2369&ask_summarization=1"},{"index":18,"title":"Faktöriyel ve Permütasyon Uygulamaları","list":{"type":"unordered","items":["Yedi kişilik bir banka, 7! (yedi faktöriyel) farklı şekilde doldurulabilir.","Yedi kişiden dört kişilik bir banka, 7P4 (yedi'nin dört'lü permütasyonu) yani 840 farklı şekilde doldurulabilir.","Farklı üç matematik, dört biyoloji ve kimya kitabı bir rafa, 12! (on iki faktöriyel) farklı şekilde sıralanabilir."]},"beginTime":2590,"endTime":2732,"href":"/video/preview/15262764232061338291?parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=P.K&t=2590&ask_summarization=1"},{"index":19,"title":"Kitap Sıralama Problemleri","list":{"type":"unordered","items":["Farklı dört matematik, altı biyoloji ve üç kimya kitabı, biyoloji kitapları yan yana olmak üzere 8!×6! farklı şekilde sıralanabilir.","Farklı altı matematik, dört biyoloji ve üç fizik kitabı, aynı tür kitaplar yan yana olmak üzere 3!×6!×4!×3! farklı şekilde sıralanabilir.","Aynı tür kitaplar yan yana ve biyoloji kitapları ortada olmak üzere sıralama, 2!×6!×4!×3! farklı şekilde yapılabilir."]},"beginTime":2732,"endTime":2906,"href":"/video/preview/15262764232061338291?parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=P.K&t=2732&ask_summarization=1"},{"index":20,"title":"Cinsiyet Sıralama Problemi","list":{"type":"unordered","items":["Yedi erkek ve altı bayanın bulunduğu bir toplulukta, aynı cinsiyetten iki kişi yan yana gelmemek üzere on üç kişilik bir koltuğa, 7!×6! farklı şekilde sıralanabilir.","Önce erkekler oturtulur ve aralarına bayanlar yerleştirilir, böylece herhangi iki erkek veya iki bayan yan yana gelmez."]},"beginTime":2906,"endTime":3017,"href":"/video/preview/15262764232061338291?parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=P.K&t=2906&ask_summarization=1"},{"index":21,"title":"Matematik ve Biyoloji Kitaplarının Sıralanması","list":{"type":"unordered","items":["Yedi farklı matematik kitabı ve dört farklı biyoloji kitabı var, biyoloji kitapları yan yana gelmemek üzere sıralanmalıdır.","Matematik kitapları 7! (yedi faktöriyel) şekilde sıralanabilir.","Biyoloji kitapları, matematik kitaplarının arasına ve uçlarına yerleştirilebilecek sekiz farklı yere 4'ü sıralanabilir, bu 8P4 (sekizin dörtlüsü permütasyon) şeklinde hesaplanır.","Sorunun cevabı 7! × 8P4 olarak bulunur."]},"beginTime":3027,"endTime":3136,"href":"/video/preview/15262764232061338291?parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=P.K&t=3027&ask_summarization=1"},{"index":22,"title":"Hüseyin ve Kaya'nın Sıralanması","list":{"type":"unordered","items":["Altı kişilik bir grupta Hüseyin ve Kaya yan yana gelmemek koşuluyla sıralanma sayısı sorulmaktadır.","Altı kişi normal şartlarda 6! (yediyüzyirmi) şekilde sıralanabilir.","Hüseyin ve Kaya yan yana geldikleri durumlar 5! × 2 = 240 farklı şekilde olabilir.","Tüm durumdan Hüseyin ve Kaya'nın yan yana geldiği durumlar çıkarıldığında 720 - 240 = 480 farklı sıralama şekli elde edilir."]},"beginTime":3136,"endTime":3245,"href":"/video/preview/15262764232061338291?parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=P.K&t=3136&ask_summarization=1"},{"index":23,"title":"Tekrarlı Permütasyon","list":{"type":"unordered","items":["Permütasyonda nesnelerin hepsi farklı değil, bazıları aynı türde olabilir.","n tane nesnenin a tanesi bir türden, b tanesi ikinci türden, c tanesi üçüncü türden ve z tanesi kinci türden olabilir.","Tekrarlı permütasyon formülü: n! / (a! × b! × c! × ... × z!)","Örnek olarak 4 kırmızı, 5 sarı ve 3 yeşil ampulün yan yana dizilme sayısı 12! / (4! × 5! × 3!) şeklinde hesaplanır."]},"beginTime":3245,"endTime":3378,"href":"/video/preview/15262764232061338291?parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=P.K&t=3245&ask_summarization=1"},{"index":24,"title":"Matematik Kelimesi Sorusu","list":{"type":"unordered","items":["Matematik sözcüğündeki harflerin yerleri değiştirilerek anlamlı ya da anlamsız dokuz harfli kaç sözcük yazılabilir sorusunun cevabı 45.360 olarak bulunmuştur.","Matematik kelimesinde iki m, iki a ve iki t harfi tekrar ettiği için faktöriyel hesaplamasında bunların tekrar sayıları dikkate alınmıştır."]},"beginTime":3401,"endTime":3515,"href":"/video/preview/15262764232061338291?parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=P.K&t=3401&ask_summarization=1"},{"index":25,"title":"Rakamlarla Sayı Oluşturma","list":{"type":"unordered","items":["9, 9, 6, 6, 6, 5, 5, 1 rakamları kullanılarak 6 ile başlayıp 1 ile biten sekiz basamaklı 90 farklı doğal sayı yazılabilir.","3325656 sayısının rakamlarının yerleri değiştirilerek 1260 farklı sekiz basamaklı sayı yazılabilir, ancak sıfırın başa gelme ihtimali çıkarıldığında 1260-420=840 sayı elde edilir."]},"beginTime":3515,"endTime":3728,"href":"/video/preview/15262764232061338291?parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=P.K&t=3515&ask_summarization=1"},{"index":26,"title":"Çift Sayı Oluşturma","list":{"type":"unordered","items":["555230 sayısının rakamları ile sekiz basamaklı 780 farklı çift doğal sayı yazılabilir.","Çift sayı olması için son rakam 0 veya 2 olmalıdır ve başa sıfır gelmemesi gerekmektedir."]},"beginTime":3728,"endTime":3908,"href":"/video/preview/15262764232061338291?parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=P.K&t=3728&ask_summarization=1"},{"index":27,"title":"Leblebi Kelimesi Sorusu","list":{"type":"unordered","items":["Leblebi kelimesinin harflerinin yerleri değiştirilerek yazılabilen anlamlı ya da anlamsız yedi harfli kelimelerin 30 tanesinde l harfi e harfini takip eder.","L ve e harfleri bir bütün olarak düşünüldüğünde geriye 5 harf kalır ve bu 5 harf 2 b ve 1 i harfi tekrar eden durumda olduğundan faktöriyel hesaplaması yapılır."]},"beginTime":3908,"endTime":3994,"href":"/video/preview/15262764232061338291?parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=P.K&t=3908&ask_summarization=1"},{"index":28,"title":"Kent Sokakları Sorusu","list":{"type":"unordered","items":["Bir kentin A noktasında bulunan bir kişi, C noktasına en kısa yolla 210 farklı şekilde gidilebilir.","Çözüm için iki yöntem gösterilmiştir: permütasyon kullanarak hesaplama veya her köşeye giden farklı yolları sayarak çözüm."]},"beginTime":3994,"endTime":4122,"href":"/video/preview/15262764232061338291?parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=P.K&t=3994&ask_summarization=1"},{"index":29,"title":"Yol Sayma Problemleri","list":{"type":"unordered","items":["Bir noktadan diğerine ulaşmak için farklı yollar bulunabilir ve bu yollar toplanarak toplam yol sayısı hesaplanabilir.","A noktasından C noktasına ulaşmak için farklı yollar bulunabilir ve bu yollar toplanarak toplam 72 farklı yolla ulaşılabilir.","A noktasından E noktasına uğrayarak C noktasına ulaşmak için 90 farklı yolla gidilebilir."]},"beginTime":4126,"endTime":4409,"href":"/video/preview/15262764232061338291?parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=P.K&t=4126&ask_summarization=1"},{"index":30,"title":"Sıralama ve Permütasyon Problemleri","list":{"type":"unordered","items":["\"LAPTO\" yazısını komşu harfleri takip ederek okumak için 6 farklı şekilde sıralanabilir.","Permütasyon problemlerinde elemanların sıralaması önemlidir ve farklı sıralamalar farklı sonuçlar verir."]},"beginTime":4409,"endTime":4493,"href":"/video/preview/15262764232061338291?parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=P.K&t=4409&ask_summarization=1"},{"index":31,"title":"Kombinasyon Kavramı","list":{"type":"unordered","items":["Kombinasyon, n elemanlı bir kümenin r elemanlı alt kümelerinin sayısını ifade eder ve P(n,r) şeklinde gösterilir.","Kombinasyon formülü: P(n,r) = n! / [(n-r)! × r!]'dır.","Kombinasyonda elemanların sıralaması önemli değildir, sadece elemanların seçilmesi önemlidir."]},"beginTime":4493,"endTime":4585,"href":"/video/preview/15262764232061338291?parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=P.K&t=4493&ask_summarization=1"},{"index":32,"title":"Kombinasyon Özellikleri","list":{"type":"unordered","items":["P(n,0) = P(n,n) = 1'dir.","P(n,1) = P(n,n-1) = n'dir.","P(n,r) = P(n,n-r)'dir.","P(n,r) + P(n,r+1) = P(n+1,r+1)'dir.","P(n,a) = P(n,b) ise ya a=b veya a+b=n'dir."]},"beginTime":4585,"endTime":4825,"href":"/video/preview/15262764232061338291?parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=P.K&t=4585&ask_summarization=1"},{"index":33,"title":"Kombinasyon Problemleri","list":{"type":"unordered","items":["Toplamın eşitliği kombinasyon kırk sorusunun cevabı onbeş olarak bulunuyor.","Kombinasyonların özellikleri kullanılarak 38. sorunun cevabı otuzaltı olarak hesaplanıyor.","39. soruda kombinasyonların toplamı 512 olarak hesaplanıyor ve x değeri 502 olarak bulunuyor."]},"beginTime":4829,"endTime":5010,"href":"/video/preview/15262764232061338291?parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=P.K&t=4829&ask_summarization=1"},{"index":34,"title":"Kombinasyon Denklemleri","list":{"type":"unordered","items":["Kombinasyon 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I hope you enjoy my video . so make sure to...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/2072031/d8eb32afc522560a2bebb884a569a9e8/564x318_1"},"target":"_self","position":"15","reqid":"1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL","summary":{"fullTextUrl":"/int_search_summary?data=http%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DqNsbNjkZLSw","linkTemplate":"/video/preview/12802124226905299881?parent-reqid=1774290111589266-12766980031990454572-balancer-l7leveler-kubr-yp-vla-24-BAL&text=P.K&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"P K logo design | illustrator logo design tutorial | adobe illustrator cc tutorial | Jakir 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