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Giải bài 5 trang 6 sách bài tập toán 10 - Cánh diều

Cho 20 điểm phân biệt. Hỏi lập được bao nhiêu vectơ khác? Biết rằng hai đầu mút của mỗi vectơ là 2 trong 20 điểm đã cho.

ᩚᩚᩚᩚᩚᩚ⁤⁤⁤⁤ᩚ⁤⁤⁤⁤ᩚ⁤⁤⁤⁤ᩚ𒀱ᩚᩚᩚTổng 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. Hỏi lập được bao nhiêu vectơ khác? Biết rằng hai đầu mút của mỗi vectơ là 2 trong 20 điểm đã cho.

Phương pháp giải - Xem chi tiết

Với 2 điểm bất kì ta lập được hai vectơ khác \(\overrightarrow 0 \). Do đó ta tìm số cách chọn từng điểm và áp dụng quy tắc nhân Bước 1: Tính số cách chọn 1 điểm đầu tiên trong 20 điểm đã cho Bước 2: Tính số cách chọn điểm thứ hai trong 19 điểm còn lại (trừ 1 điểm đã chọn ở bước 1) Bước 3: Áp dụng quy tắc nhân để tính tổng số vectơ được lập ra   

Lời giải chi tiết

Việc chọn hai điểm phân biệt trong số 20 điểm phân biệt để lập thành một vectơ là thực hiện hai hành động liên tiếp: chọn một điểm đầu tiên, sau đó chọn một điểm còn lại.Có 20 cách chọn một điểm đầu tiên trong số 20 điểm phân biệt.Vì ta đã chọn một điểm trên nên bây giờ ta chỉ còn 19 điểm phân biệt. Vì vậy lúc này có 19 cách chọn một điểm còn lại.Vậy ta có thể lập được tất cả 20.19 = 380 vectơ khác \(\overrightarrow 0 \) từ 20 điểm đã cho.

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