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Câu 15 trang 64 SGK Đại số và Giải tích 11 Nâng cao

Một tổ có 8 em nam và 2 em nữ. Người ta cần chọn ra 5 em trong tổ tham dự cuộc thi học sinh thanh lịch của trường. Yêu cầu trong các em được chọn, phải có ít nhất một em nữ. Hỏi có bao nhiêu cách chọn ?
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Đề bài

Một tổ có 8 em nam và 2 em nữ. Người ta cần chọn ra 5 em trong tổ tham dự cuộc thi học sinh thanh lịch của trường. Yêu cầu trong các em được chọn, phải có ít nhất một em nữ. Hỏi có bao nhiêu cách chọn?

Lời giải chi tiết

Số cách chọn 5 em trong 10 em là :\(C_{10}^5.\)Số cách chọn 5 em toàn nam là : \(C_{8}^5.\)Do đó số cách chọn ít nhất một nữ là :   \(C_{10}^5 - C_8^5 = 196.\)

Cách khác:

Các em có thể tính trực tiếp như sau:TH1: Có 1 nữ, 4 namChọn 1 nữ có 2 cách.Chọn 4 trong 8 nam có \(C_8^4 = 70\) cách chọn.Theo quy tắc nhân có 2.70=140 cách chọn.TH2: Có 2 nữ, 3 nam.Chọn 2 nữ có 1 cách.Chọn 3 trong 8 nam có \(C_8^3 = 56\) cách chọn.Theo quy tắc nhân có 1.56=56 cách chọn.Vậy theo quy tắc cộng có: 140+56=196 cách chọn.

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