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matematik veya fizik sorularından birini çözdükten sonra tarih sorularından birini çözecektir.","Matematik veya fizik sorularından birini seçmek için 4+3=7 farklı şekilde seçilebilir, tarih sorularından birini seçmek için 8 farklı şekilde seçilebilir, toplam 7×8=56 farklı şekilde seçilebilir."]},"beginTime":852,"endTime":915,"href":"/video/preview/7916236160910232866?parent-reqid=1770014308203048-1474254906438368391-balancer-l7leveler-kubr-yp-klg-153-BAL&text=SaymMAN&t=852&ask_summarization=1"},{"index":8,"title":"Matematik Problemlerinde Mantık Kullanımı","list":{"type":"unordered","items":["Matematik problemlerinde kendi hikayeler yazmak yerine mantık kullanmak önemlidir.","Matematik veya fizik sorularından birini çözdükten sonra kesin tarih sorusu çözülmesi gerektiği belirtilmiştir.","Matematik sorusu çözebileceği 4 adet, tarih sorusu çözebileceği 8 adet farklı durum vardır ve toplam 56 farklı çözüm 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Problemi","list":{"type":"unordered","items":["Dört kişi yan yana duran tek kişilik altı sandalyeye oturma problemi çözülüyor.","İlk kişi için 6 farklı sandalye seçeneği, ikinci kişi için 5, üçüncü kişi için 4, dördüncü kişi için 3 sandalye seçeneği var.","Toplam 6×5×4×3 = 360 farklı şekilde kişiler sandalyelere oturabilir."]},"beginTime":1301,"endTime":1419,"href":"/video/preview/7916236160910232866?parent-reqid=1770014308203048-1474254906438368391-balancer-l7leveler-kubr-yp-klg-153-BAL&text=SaymMAN&t=1301&ask_summarization=1"},{"index":13,"title":"Takım Seçimi Problemi","list":{"type":"unordered","items":["Onbir kişilik bir takımdan bir kaptan, bir kaptan yardımcısı ve üçüncü bir kaptan seçme problemi çözülüyor.","Üçüncü kaptan belli olduğunda, kalan 10 kişiden kaptan seçilebilir.","Toplam 10×9 = 90 farklı şekilde kaptan, kaptan yardımcısı ve üçüncü kaptan seçilebilir."]},"beginTime":1419,"endTime":1518,"href":"/video/preview/7916236160910232866?parent-reqid=1770014308203048-1474254906438368391-balancer-l7leveler-kubr-yp-klg-153-BAL&text=SaymMAN&t=1419&ask_summarization=1"},{"index":14,"title":"Kare Boyama Problemi","list":{"type":"unordered","items":["Yirmibeş birim kareye ayrılmış bir karenin her satırı ve sütunu yalnız bir kere boyanarak desen elde edilmesi problemi çözülüyor.","İlk satır için 5 farklı boyama seçeneği, ikinci satır için 4, üçüncü satır için 3, dördüncü satır için 2, beşinci satır için 1 seçenek var.","Toplam 5×4×3×2×1 = 5! = 120 farklı şekilde desen oluşturulabilir."]},"beginTime":1518,"endTime":1635,"href":"/video/preview/7916236160910232866?parent-reqid=1770014308203048-1474254906438368391-balancer-l7leveler-kubr-yp-klg-153-BAL&text=SaymMAN&t=1518&ask_summarization=1"},{"index":15,"title":"Sınav Cevap Anahtarı Sorusu","list":{"type":"unordered","items":["Her biri üç seçenekli olan on sorudan oluşan bir sınavın cevap anahtarı oluşturulacak ve kaç farklı cevap anahtarı oluşturulabilir sorusu çözülüyor.","A seçeneğinde, her soru için üç farklı seçenek olduğu için cevap anahtarı 3 üzeri 10 farklı şekilde oluşturulabilir.","B seçeneğinde, arka arkaya gelen iki sorunun cevabı aynı seçenek olmayacak şekilde cevap anahtarı oluşturulduğunda, çözüm 3×2 üzeri 9 şeklinde hesaplanır."]},"beginTime":1639,"endTime":1832,"href":"/video/preview/7916236160910232866?parent-reqid=1770014308203048-1474254906438368391-balancer-l7leveler-kubr-yp-klg-153-BAL&text=SaymMAN&t=1639&ask_summarization=1"},{"index":16,"title":"Dersin Sonu ve Ödev","list":{"type":"unordered","items":["Birinci ünite birinci ders tamamlanıyor ve kan takviminde ilk tik atılıyor.","Öğrenciden \"Soru Avcısı Sınav Provası\" kitabındaki birinci ünite birinci ders sayfasındaki altı ödev sorusunu çözmesi isteniyor.","Öğretmen, öğrenciyi ilk on bine yazdırmak hedefiyle ikinci derste aynı enerjiyle beklediğini 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This is Me @SaymanRifat an App Developer. Thanks to 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Öğretmen, \"tanımlar, kavramlar, ispatlar\" sloganıyla matematiği en temelden zirveye giden yolda yeniden başlattığını belirtmektedir.","Video, 10. sınıf matematik müfredatının ilk konusu olan \"Sayma ve Olasılık\" ile başlayıp, özellikle \"Toplama ve Çarpma Yoluyla Sayma\" konusunu ele almaktadır. Öğretmen, toplama yoluyla sayma ve çarpma yoluyla sayma kavramlarını günlük hayattan örneklerle açıklamakta, ardından 15 soru üzerinden konuyu pekiştirmektedir.","Videoda başkan yardımcısı seçimi, mektup-posta kutusu problemi, sandalye oturma düzeni ve grup seçimi gibi çeşitli kombinasyon problemleri çözülmektedir. Öğretmen, bir sonraki derste yol soruları, küme soruları ve yazma soruları gibi çarpma yoluyla sayma konusunun diğer tiplerini anlatacağını belirtmektedir."]},"endTime":1812,"title":"10. Sınıf Matematik Dersi: Sayma ve Olasılık","beginTime":0}],"fullResult":[{"index":0,"title":"Rehber Matematik 10. Sınıf Yeni Sezon Açılışı","list":{"type":"unordered","items":["Rehber Matematik'te 10. sınıf matematik müfredatının ilk konusu olan sayma olasılığı ile yeni bir sezon başlıyor.","Matematik dersinde tanımlar, kavramlar ve ispatlar sloganıyla birlikte en temelden zirveye giden yolda ilerlenecek.","Konu anlatımı kısa olmasına rağmen, bol örnek çözmek konuyu anlamak için çok önemlidir."]},"beginTime":0,"endTime":103,"href":"/video/preview/6452280751225853702?parent-reqid=1770014308203048-1474254906438368391-balancer-l7leveler-kubr-yp-klg-153-BAL&text=SaymMAN&t=0&ask_summarization=1"},{"index":1,"title":"Saymanın Temel İlkeleri","list":{"type":"unordered","items":["Sayma konusunda toplama yoluyla sayma ve çarpma yoluyla sayma olmak üzere iki temel ilke vardır.","Toplama yoluyla sayma, \"veya\" kelimesiyle belirtilen durumlarda kullanılır ve işlemler toplama işlemiyle birleştirilir.","Çarpma yoluyla sayma, \"ve\" bağlacı ile belirtilen durumlarda kullanılır ve işlemler çarpma işlemiyle 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Edirne'ye beş farklı karayolu şirketi, dört farklı demiryolu şirketi ve üç farklı havayolu şirketi ile gidilebilmektedir.","Toplama ve çarpma yöntemleriyle sayma arasında fark vardır; farklı seçenekler arasında \"veya\" bağlacı varsa toplama, \"ve\" bağlacı varsa çarpma işlemi yapılır.","Muğla'dan Edirne'ye gidilebilecek toplam farklı yol sayısı 5+4+3=12'dir."]},"beginTime":460,"endTime":632,"href":"/video/preview/6452280751225853702?parent-reqid=1770014308203048-1474254906438368391-balancer-l7leveler-kubr-yp-klg-153-BAL&text=SaymMAN&t=460&ask_summarization=1"},{"index":4,"title":"Okul Komisyonu Sorusu","list":{"type":"unordered","items":["Bir ilçede dört farklı okul vardır; her okulda bir müdür, üç müdür yardımcısı ve beş öğretmen bulunmaktadır.","Bir komisyon için bir müdür, bir müdür yardımcısı ve bir öğretmen seçilecektir.","Toplam farklı komisyon seçme ihtimali 4×8×20=640'dır."]},"beginTime":632,"endTime":727,"href":"/video/preview/6452280751225853702?parent-reqid=1770014308203048-1474254906438368391-balancer-l7leveler-kubr-yp-klg-153-BAL&text=SaymMAN&t=632&ask_summarization=1"},{"index":5,"title":"Ayakkabı Mağazası Sorusu","list":{"type":"unordered","items":["Bir mağazada üç çeşit spor, beş çeşit yürüyüş ve dört çeşit klasik ayakkabı bulunmaktadır.","Necati bir çeşit yürüyüş ve bir çeşit spor ayakkabı alacaktır (5×3=15 farklı ihtimal).","Remzi ise bir çeşit spor veya bir çeşit klasik ayakkabı seçecektir (3+4=7 farklı ihtimal).","Necati ve Remzi'nin toplam seçim sayısı 15+7=22'dir."]},"beginTime":727,"endTime":860,"href":"/video/preview/6452280751225853702?parent-reqid=1770014308203048-1474254906438368391-balancer-l7leveler-kubr-yp-klg-153-BAL&text=SaymMAN&t=727&ask_summarization=1"},{"index":6,"title":"Lokanta Sorusu","list":{"type":"unordered","items":["Bir lokantada iki çeşit çorba, üç ana yemek ve beş tatlı bulunmaktadır.","Remzi çorba veya ana yemekten birini yiyip sonra bir tatlı yiyecektir.","Toplam farklı yemek seçme ihtimali (2+3)×5=25'tir."]},"beginTime":860,"endTime":946,"href":"/video/preview/6452280751225853702?parent-reqid=1770014308203048-1474254906438368391-balancer-l7leveler-kubr-yp-klg-153-BAL&text=SaymMAN&t=860&ask_summarization=1"},{"index":7,"title":"Çarpma Yöntemiyle Sayma - İkinci Tip Problemler","list":{"type":"unordered","items":["Sekiz kişilik bir takımdan önce başkan, sonra yardımcısı seçilecektir.","Başkan seçme ihtimali 8'dir.","Yaptığınız seçimlere devam ediyorsanız, araya çarpma işlemi konulur."]},"beginTime":946,"endTime":982,"href":"/video/preview/6452280751225853702?parent-reqid=1770014308203048-1474254906438368391-balancer-l7leveler-kubr-yp-klg-153-BAL&text=SaymMAN&t=946&ask_summarization=1"},{"index":8,"title":"Basınak ve Başkan Yardımcısı Seçimi","list":{"type":"unordered","items":["Bir grup içinde başkan seçildikten sonra başkan yardımcısı seçimi yapılıyor, ancak başkan aynı zamanda 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Matematik ile 10.Sınıf Matematik konularını yeniliyoruz!! MatBook 10 ile. 1.Ünite Sayma ve Olasılık 1.Ders Konumuz Sayma Saymanın Temel İlkeleri Toplama Yoluyla Sayma Çarpma Yoluyla Sayma...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/2755728/2530820e051f5cd55a48d74fd22032a1/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/_j79PQIAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"19","reqid":"1770014308203048-1474254906438368391-balancer-l7leveler-kubr-yp-klg-153-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1770014308203048-1474254906438368391-balancer-l7leveler-kubr-yp-klg-153-BAL&text=videoid:12038390426195149236","teaser":[{"list":{"type":"unordered","items":["Bu video, Deniz Sercan Hoca tarafından sunulan 10. sınıf matematik dersinin sayma ve olasılık ünitesinin ilk bölümüdür. Hoca, Mehmet Hoca'nın kardeşi olarak tanıtılmaktadır.","Video, toplama yoluyla sayma ve çarpma yoluyla sayma kavramlarını matematiksel tanımlarla açıklamakta ve günlük hayattan örneklerle pekiştirmektedir. İçerik, basit örneklerle başlayıp zamanla soru çeşitlerini değiştirerek ilerlemekte, bağlı olaylar ve bağımsız olaylar için çarpma ve toplama metodlarının nasıl kullanılacağını adım adım göstermektedir.","Videoda giyim eşyaları seçimi, kurum çalışanları, lokanta menüsü, sınav soruları, takım kaptanları ve mektup-posta kutusu gibi çeşitli günlük hayattan örnekler bulunmaktadır. Ayrıca, 10 soruluk bir sınavın cevap anahtarı oluşturma problemi de ele alınmaktadır. Video, 14 derse kadar sürecek bir kamp kapsamında hazırlanmıştır."]},"endTime":1623,"title":"10. Sınıf Matematik: Sayma Yöntemleri","beginTime":0}],"fullResult":[{"index":0,"title":"10. Sınıf Matematik Dersi Tanıtımı","list":{"type":"unordered","items":["Deniz Serkan Hoca, 10. sınıf matematik derslerini başlatıyor ve Rehber Matematik'in Matbook kitabını kullanarak derslerini sunuyor.","Matbook kitabının iki parçadan oluştuğu belirtiliyor: birinci kitap video ders notları, ikinci kitap ise soru avcısı.","Derslerde öğrencilere not almayı, soruları çözüyormuş gibi yapmayı ve \"sıra sende\" dediğinde videoyu durdurup kendi çözmelerini öneriyor."]},"beginTime":0,"endTime":140,"href":"/video/preview/12038390426195149236?parent-reqid=1770014308203048-1474254906438368391-balancer-l7leveler-kubr-yp-klg-153-BAL&text=SaymMAN&t=0&ask_summarization=1"},{"index":1,"title":"Toplama Yoluyla Sayma","list":{"type":"unordered","items":["Toplama yoluyla sayma, ayrık iki olaydan birincisi n farklı şekilde, ikincisi m farklı şekilde gerçekleşiyorsa, bu olaylardan birincisi veya ikincisi m+n farklı şekilde gerçekleşir.","Toplama yoluyla saymada en önemli kriter, olayların birbirlerinden bağımsız olması ve soru kökeninde \"veya\" kelimesinin bulunmasıdır.","Örnek olarak, gardırobunda 5 gömlek ve 4 tişört olan bir kişi, \"veya\" kelimesi olduğu için toplama yoluyla 9 farklı şekilde kıyafet seçebilir."]},"beginTime":140,"endTime":226,"href":"/video/preview/12038390426195149236?parent-reqid=1770014308203048-1474254906438368391-balancer-l7leveler-kubr-yp-klg-153-BAL&text=SaymMAN&t=140&ask_summarization=1"},{"index":2,"title":"Çarpma Yoluyla Sayma","list":{"type":"unordered","items":["Çarpma yoluyla sayma, iki olaydan birincisi n farklı şekilde, ikincisi birinci olaya bağlı olarak m farklı şekilde gerçekleşiyorsa, bu olaylardan birincisi ve ikincisi m×n farklı şekilde gerçekleşir.","Çarpma yoluyla saymada en önemli kriter, olayların birbirlerine bağlı olması ve soru kökeninde \"ve\" kelimesinin bulunmasıdır.","Örnek olarak, 5 gömlek ve 4 pantolon arasından bir gömlek ve bir pantolon seçmek isteyen bir kişi, \"ve\" kelimesi olduğu için çarpma yoluyla 20 farklı şekilde giyinebilir."]},"beginTime":226,"endTime":268,"href":"/video/preview/12038390426195149236?parent-reqid=1770014308203048-1474254906438368391-balancer-l7leveler-kubr-yp-klg-153-BAL&text=SaymMAN&t=226&ask_summarization=1"},{"index":3,"title":"Örnek Sorular","list":{"type":"unordered","items":["Birinci örnek soruda, 15 kız ve 12 erkek öğrenci arasından \"veya\" kelimesi olduğu için toplama yoluyla 27 farklı şekilde bir öğrenci seçilebilir.","İkinci örnek soruda, 5 oyuncak araba, 4 puzzle ve 3 lego arasından \"veya\" kelimesi olduğu için toplama yoluyla 12 farklı şekilde bir oyuncak seçilebilir.","Üçüncü örnek soruda, 5 gömlek ve 4 pantolon arasından \"ve\" kelimesi olduğu için çarpma yoluyla 20 farklı şekilde bir gömlek ve pantolon seçilebilir.","Dördüncü örnek soruda, 5 gömlek, 4 pantolon ve 2 ayakkabı arasından \"ve\" kelimesi olduğu için çarpma yoluyla 40 farklı şekilde bir kıyafet seçilebilir.","Beşinci örnek soruda, 5 farklı kurumda birer müdür, asistan ve çalışan olup \"ve\" kelimesi olduğu için çarpma yoluyla 1500 farklı şekilde bir müdür, asistan ve çalışan seçilebilir."]},"beginTime":268,"endTime":582,"href":"/video/preview/12038390426195149236?parent-reqid=1770014308203048-1474254906438368391-balancer-l7leveler-kubr-yp-klg-153-BAL&text=SaymMAN&t=268&ask_summarization=1"},{"index":4,"title":"Sayma Metotları ve Örnekler","list":{"type":"unordered","items":["Ahmet dört ana yemekten birini seçebilir ve çarpma metoduyla 4×5=20 farklı şekilde seçim yapabilir.","Buğra ya bir çorba veya bir tatlı yiyebilir, toplama metoduyla 5+3=8 farklı şekilde yiyecek seçimi yapabilir.","Ahmet matematik veya fizik sorularından birini çözdükten sonra tarih sorularından birini çözecek, toplama ve çarpma metodlarıyla 7×8=56 farklı şekilde seçim yapabilir."]},"beginTime":583,"endTime":692,"href":"/video/preview/12038390426195149236?parent-reqid=1770014308203048-1474254906438368391-balancer-l7leveler-kubr-yp-klg-153-BAL&text=SaymMAN&t=583&ask_summarization=1"},{"index":5,"title":"Çarpma Yöntemi ile Sayma","list":{"type":"unordered","items":["Altı kişilik bir takımdan önce bir kaptan, sonra bir kaptan yardımcısı seçilecek, bağlı olaylar olduğu için çarpma metoduyla 6×5=30 farklı şekilde seçim yapılabilir.","Dört mektup ve beş posta kutusu var, her mektup farklı bir posta kutusuna atılacak şartıyla 5×4×3×2=120 farklı şekilde atılabilir.","Dört kişi yan yana duran altı sandalyede oturacak, bağlı olaylar olduğu için çarpma metoduyla 6×5×4×3=360 farklı şekilde oturabilirler."]},"beginTime":692,"endTime":1064,"href":"/video/preview/12038390426195149236?parent-reqid=1770014308203048-1474254906438368391-balancer-l7leveler-kubr-yp-klg-153-BAL&text=SaymMAN&t=692&ask_summarization=1"},{"index":6,"title":"Kaptan Seçimi Problemi","list":{"type":"unordered","items":["12 kişilik bir takımdan kaptan, kaptan yardımcısı ve üçüncü kaptan seçilecek.","Üçüncü kaptanın kim olduğu biliniyor, geriye kalan 11 kişiden kaptan ve kaptan yardımcısı seçilecek.","Seçimler çarpma yoluyla hesaplanarak 10 × 9 = 90 farklı şekilde yapılabilir."]},"beginTime":1069,"endTime":1187,"href":"/video/preview/12038390426195149236?parent-reqid=1770014308203048-1474254906438368391-balancer-l7leveler-kubr-yp-klg-153-BAL&text=SaymMAN&t=1069&ask_summarization=1"},{"index":7,"title":"Kare Şekli Boyama Problemi","list":{"type":"unordered","items":["5×5 birim kareye ayrılmış bir karede, her satır ve sütundan yalnız bir kare boyanacak.","İlk satırda 5 seçenek, ikinci satırda 4 seçenek, üçüncü satırda 3 seçenek, dördüncü satırda 2 seçenek ve beşinci satırda 1 seçenek bulunuyor.","Toplam 5 × 4 × 3 × 2 × 1 = 120 farklı desen oluşturulabilir."]},"beginTime":1187,"endTime":1336,"href":"/video/preview/12038390426195149236?parent-reqid=1770014308203048-1474254906438368391-balancer-l7leveler-kubr-yp-klg-153-BAL&text=SaymMAN&t=1187&ask_summarization=1"},{"index":8,"title":"Cevap Anahtarı Oluşturma Problemi","list":{"type":"unordered","items":["10 sorudan oluşan bir sınavın her sorusunda 3 seçenek 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sağlanabilir."]},"beginTime":1518,"endTime":1588,"href":"/video/preview/12038390426195149236?parent-reqid=1770014308203048-1474254906438368391-balancer-l7leveler-kubr-yp-klg-153-BAL&text=SaymMAN&t=1518&ask_summarization=1"}],"linkTemplate":"/video/preview/12038390426195149236?parent-reqid=1770014308203048-1474254906438368391-balancer-l7leveler-kubr-yp-klg-153-BAL&text=SaymMAN&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Sayma ve Olasılık 1 | Toplama ve Çarpma Yoluyla Sayma 1 | 10.Sinif Matematik MatBook | 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