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Giải bài 1 trang 32 SGK Toán 10 tập 2 – Chân trời sáng tạo

Cần xếp một nhóm 5 học sinh ngồi vào một dãy 5 chiếc ghế

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

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

Cần xếp một nhóm 5 học sinh ngồi vào một dãy 5 chiếc ghế a) Có bao nhiêu cách sắp xếp? b) Nếu bạn Nga (một thành viên trong nhóm) nhất định muốn ngồi vào chiếc ghế ngoài cùng bên trái, thì có bao nhiêu cách sắp xếp?

Phương pháp giải - Xem chi tiết

a) Tính hoán vị của 5 bạn học sinh b) Tính hoán vị của 4 bạn học sinh

Lời giải chi tiết

a) Mỗi cách sắp xếp 5 bạn học sinh vào 5 chiếc ghế là một hoán vị của 5 bạn học sinh. Do đó, số cách sắp xếp 5 bạn học sinh ngồi vào 5 cái ghế là hoán vị là:                   \({P_5} = 5!\) (cách)b) Khi bạn Nga nhất định ngồi vào chiếc ghế ngoài cùng bên trái, thì số cách sắp xếp là số cách sắp xếp 4 bạn còn lại vào 4 chiếc ghế, mỗi cách như vậy là một hoán vị của 4 bạn học sinh. Do đó, số cách sắp xếp là:                             \({P_4} = 4! = 24\) (cách)

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