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Giải bài 41 trang 17 sách bài tập toán 10 - Cánh diều

Cho 20 điểm phân biệt và không có ba điểm nào thẳng hàng. Lập được bao nhiêu tam giác có 3 đỉnh là 3 điểm trong 20 điểm đã cho?

💎Tổng 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

Cho 20 điểm phân biệt và không có ba điểm nào thẳng hàng. Lập được bao nhiêu tam giác có 3 đỉnh là 3 điểm trong 20 điểm đã cho? A. 1 140                      B. 6                             C. 6 840                      D. 8 000

Phương pháp giải - Xem chi tiết

Do không có 3 điểm nào thẳng hàng nên lấy 3 điểm bất kì trong tổng số các điểm đã cho lập được một tam giác. Do đó ta áp dụng tổ hợp

Lời giải chi tiết

Trong 20 điểm phân biệt không có ba điểm nào thẳng hàng nên cứ lấy 3 điểm bất kì trong 20 điểm phân biệt ta được một tam giácMỗi cách chọn 3 điểm trong 20 điểm phân biệt đã cho là một tổ hợp chập 3 của 20.Số cách chọn 3 điểm trong 20 điểm đã cho là \(C_{20}^3 = 1140\)

® Chọn A

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