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Câu 10 trang 63 SGK Đại số và Giải tích 11 Nâng cao

Có bao nhiêu số tự nhiên có 6 chữ số và chia hết cho 5 ?
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Đề bài

Có bao nhiêu số tự nhiên có 6 chữ số và chia hết cho 5 ?

Phương pháp giải - Xem chi tiết

Số chia hết cho 5 thì có chữ số tận cùng bằng 0 hoặc 5. Đếm số cách chọn của mỗi chữ số và dùng quy tắc nhân.

Lời giải chi tiết

Gọi số A có 6 chữ số cần tìm có dạng \(\overline {abcdeg }, (a \ne 0) \)+) a khác 0 nên a có 9 cách chọn {1,2,..,9}+) A chia hết cho 5 nên chữ số tận cùng \(g \in {0;5}\). Vậy g có 2 cách chọn.+) Các chữ số b, c, d, e mỗi chữ số có 10 cách chọn {0,1,2,...,9}Theo quy tắc nhân ta có : \(9.10.10.10.10.2 = 180000\) sốVậy có 180000 số có 6 chữ số chia hết cho 5.

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