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Giải bài 3 trang 14 SGK Toán 10 tập 2 – Cánh diều

Bạn Việt chọn mật khẩu cho email của mình là một dãy gồm 8 kí tự đổi một khác nhau, trong đó có 3 kí tự đầu tiên là 3 chữ cái trong bảng gồm 26 chữ cái in thường và 5 kí tự tiếp theo là chữ số

🅘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

Bạn Việt chọn mật khẩu cho email của mình là một dãy gồm 8 kí tự đổi một khác nhau, trong đó có 3 kí tự đầu tiên là 3 chữ cái trong bảng gồm 26 chữ cái in thường 𒐪và 5 kí tự tiếp theo là chữ số. Bạn Việt có bao nhiêu cách tạo ra mật khẩu?

Phương pháp giải - Xem chi tiết

B1: Chọn 3 kí tự đầu tiên là 3 chữ cái trong bảng gồm 26 chữ cái in thường rồi sắp xếp thứ tự \( \Rightarrow \) sử dụng công thức chỉnh hợp B2: Chọn 5 kí tự tiếp theo là chữ số và sắp xếp thứ tự \( \Rightarrow \) sử dụng công thức chỉnh hợp B3: Áp dụng quy tắc nhân

Lời giải chi tiết

+) Số cách chọn 3 kí tự đầu tiên là 3 chữ cái trong bảng gồm 26 chữ cái in thường là: \(A_{26}^3\) (cách)+) Số cách chọn 5 kí tự tiếp theo là chữ số là: \(A_{10}^5\) (cách)+) Áp dụng quy tắc nhân, số mật khẩu Việt có thể tạo ra là: \(A_{26}^3.A_{10}^5\)(mật khẩu)

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