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Giải bài 3 trang 32 SGK Toán 10 tập 2 – Chân trời sáng tạo

Tổ 1 có 4 bạn nam và 5 bạn nữ. Có bao nhiêu cách cử 3 bạn của tổ làm trực nhật trong mỗi trường hợp như sau? a) 3 bạn được chọn bất kỳ b) 3 bạn gồm 2 nam và 1 nữ

♐Tổng hợp đề thi học kì 2 lớp 10 tất cả các môn - Chân trời sáng tạo

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Đề bài

Tổ 1 có 4 bạn nam và 5 bạn nữ. Có bao nhiêu cách cử 3 bạn của tổ làm trực nhật trong mỗi trường hợp như sau? a) 3 bạn được chọn bất kỳ b) 3 bạn gồm 2 nam và 1 nữ

Phương pháp giải - Xem chi tiết

a) Tính tổ hợp chập 3 của 9 b)       Bước 1: Chọn 2 bạn nam từ 4 bạn nam đã cho           Bước 2: Chọn 1 bạn nữ từ 5 bạn đã cho           Bước 3: Áp dụng quy tắc nhân

Lời giải chi tiết

a) Mỗi cách chọn 3 bạn từ 9 bạn trong tổ một đi trực nhật là một tổ hợp chập 3 của 9. Do đó, số cách cử 3 bạn bất kì đi trực nhật là:                             \(C_9^3 = \frac{{9!}}{{3!.6!}} = 84\) (cách)b) Mỗi cách chọn 3 bạn gồm 2 nam và 1 nữ đi trực nhật gồm 2 công đoạn:          Công đoạn 1: Chọn 2 bạn namMỗi cách chọn 2 bạn nam từ 4 bạn nam đã cho là một tổ hợp chập 2 của 4. Do đó, số cách chọn 2 bạn nam từ 4 bạn nam đã cho là:        \(C_4^2 = \frac{{4!}}{{2!.2!}} = 6\) (cách)          Công đoạn 2: Chọn 1 bạn nữa trong 5 bạn đã cho, có 5 cáchÁp dụng quy tắc nhân, ta có số các cử 3 bạn đi trực nhật trong đó 2 nam và 1 nữ là:                             \(6.5 = 30\) (cách)

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