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Giải bài 5 trang 14 SGK Toán 10 tập 2 – Cánh diều

Một nhóm 22 bạn đi chụp ảnh kỉ yếu. Nhóm muốn trong bức ảnh có 7 bạn ngồi ở hàng đầu và 15 bạn đứng ở hàng sau. Có bao nhiêu cách xếp vị trí chụp ảnh như vậy?

ౠTổng hợp đề thi 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

Một nhóm 22 bạn đi chụp ảnh kỉ yếu. Nhóm muốn trong bức ảnh có 7 bạn ngồi ở hàng đầu và 15 bạn đứng ở hàng sau. Có bao nhiêu cách xếp vị trí chụp ảnh như vậy?

Phương pháp giải - Xem chi tiết

B1: Chọn 7 bạn từ 22 bạn rồi sắp xếp thứ tự vào hàng đẩu \( \Rightarrow \) sử dụng công thức chỉnh hợp. B2: Sắp xếp 15 bạn còn lại vào hàng sau \( \Rightarrow \) Sử dụng công thức hoán vị. B3: Áp dụng quy tắc nhân.

Lời giải chi tiết

Cách 1: +) Số cách chọn 7 bạn ngồi ở hàng đầu là: \(A_{22}^7\) (cách). +) Số cách sắp xếp 15 bạn còn lại vào hàng sau là: \({P_{15}} = 15!\) (cách). +) Áp dụng quy tắc nhân, số cách xếp vị trí chụp ảnh là: \(A_{22}^7.15!\) (cách). Cách 2: Vì 22 bạn học sinh có vai trò như nhau và vị trí ngồi trên, đứng dưới có vai trò như nhau nên số cách xếp 22 bạn vào 22 vị trí khác nhau là 22! (cách)

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