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Giải bài 8 trang 6 sách bài tập toán 10 - Cánh diều

Trong loạt đá luân lưu giữa hai đội tuyển, huấn luyện viên của một đội phải lập danh sách 5 cầu thủ từ 11 cầu thủ trên sân và xếp thứ tự đá luân lưu của họ. Hỏi huấn luyện viên có bao nhiêu cách lập một danh sách cầu thủ đá luân lưu? Biết ông sẽ để đội trưởng là người sút lượt thứ nhất và tiền đạo cắm (không phải đội trưởng) là người sút lượt thứ ba.

Tổng hợp đề t𒁃hi học kì 2 lớp 10 tất cả các môn - Cánh diều

Toán - Văn - Anh - Lí - Hóa - Sinh - Sử - Địa...
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Đề bài

Trong loạt đá luân lưu giữa hai đội tuyển, huấn luyện viên của một đội phải lập danh sách 5 cầu thủ từ 11 cầu thủ trên sân và xếp thứ tự đá luân lưu của họ. Hỏi huấn luyện viên có bao nhiêu cách lập một danh sách cầu thủ đá luân lưu? Biết ông sẽ để đội trưởng là người sút lượt thứ nhất và tiền đạo cắm (không phải đội trưởng) là người sút lượt thứ ba.

Phương pháp giải - Xem chi tiết

Ta lựa chọn từng cầu thủ theo từng bước liên tiếp ứng với điều kiện đã cho Bước 1: Tính số cách chọn 1 cầu thủ đá lượt thứ hai trong 9 cầu thủ (trừ đội trưởng và tiền đạo cắm) Bước 2: Tính số cách chọn 1 cầu thủ đá lượt thứ tư trong 8 cầu thủ (trừ đội trưởng, tiền đạo cắm và 1 cầu thủ được chọn ở bước 1) Bước 3: Tính số cách chọn 1 cầu thủ đá lượt thứ năm trong 7 cầu thủ (trừ đội trưởng, tiền đạo cắm và 2 cầu thủ được chọn ở hai bước trên) Bước 4: Áp dụng quy tắc nhân để tính tổng số cách chọn  

Lời giải chi tiết

Vì đội trưởng là người sút lượt thứ nhất và tiền đạo cắm là người sút lượt thứ ba nên chỉ còn 3 lượt sút thứ hai, thứ tư và thứ năm cần sắp xếp.Sau khi xếp lượt sút của đội trưởng và tiền đạo cắm thì còn 9 cầu thủ để huấn luyện viên lựa chọn.Việc chọn 3 cầu thủ trong số 9 cầu thủ và xếp thứ tự đá luân lưu của họ là thực hiện 3 hành động liên tiếp: chọn cầu thủ sút lượt thứ hai, sau đó chọn cầu thủ sút lượt thứ tư và cuối cùng là chọn cầu thủ sút lượt thứ năm.Huấn luyện viên có 9 cách chọn một cầu thủ sút lượt thứ hai.Vì huấn luyện viên đã chọn một cầu thủ sút lượt thứ hai, nên lúc này ông có 8 cách chọn một cầu thủ sút lượt thứ tư.Vì huấn luyện viên đã chọn hai cầu thủ sút lượt thứ hai và thứ tư, nên lúc này ông có 7 cách chọn một cầu thủ sút lượt thứ năm.Vậy huấn luyện viên có tất cả 9.8.7 = 504 cách lập một danh sách 5 cầu thủ đá luân lưu. 

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