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Giải bài 8.4 trang 65 SGK Toán 10 – Kết nối tri thức

Có bao nhiêu số tự nhiên

🔯Tổng hợp đề thi học kì 2 lớp 10 tất cả các môn - Kết nối tri thức

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

Có bao nhiêu số tự nhiên a) có 3 chữ số khác nhau b) là số lẻ có 3 chữ số khác nhau? c) là số có 3 chữ số và chia hết cho 5? d) là số có 3 chữ số khác nhau và chia hết cho 5?

Phương pháp giải - Xem chi tiết

Áp dụng kết hợp quy tắc cộng và quy tắc nhân.

Lời giải chi tiết

๊Chọn các chữ số hàng trăm, hàng chục, hàng đơn vị trong các chữ số 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

a) - chữ số hàng trăm có 9 cách (khác 0)

♊- chữ số hàng chục có 9 cách (khác chữ số hàng trăm)

⭕- chữ số hàng đơn vị có 8 cách (khác chữ số hàng trăm và hàng chục)

ᩚᩚᩚᩚᩚᩚ⁤⁤⁤⁤ᩚ⁤⁤⁤⁤ᩚ⁤⁤⁤⁤ᩚ𒀱ᩚᩚᩚVậy có tất cả 9. 9. 8= 648 số tự nhiên có 3 chữ số khác nhau.

b) - Chọn chữ số hàng đơn vị có 5 cách 

- Chọn chữ số hàng trăm có 8 cách

- Chọn chữ số hàng chục có 8 cách 

💙Vậy có tất cả 5. 8. 8= 320 số lẻ có 3 chữ số khác nhau.

c) - Chọn chữ số hàng đơn vị có 2 cách 

- Chọn chữ số hàng trăm có 9 cách

- Chọn chữ số hàng chục có 10 cách

♈Vậy có tất cả 2.9.10= 180 số tự nhiên có 3 chữ số chia hết cho 5.

d) Trường hợp 1: chữ số hàng đơn vị là 0.

- Chọn chữ số hàng trăm có 9 cách 

- Chọn chữ số hàng chục có 8 cách

Trường hợp 2 chữ số hàng đơn vị là 5:

- Chọn chữ số hàng trăm có 8 cách (khác 0 và 5)

- Chọn chữ số hàng chục có 8 cách

☂Vậy có tất cả 9.8 +8. 8= 136 số tự nhiên có 3 chữ số khác nhau  và chia hết cho 5.


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