AMC 8 2015 Problem 10
AMC8 2015 年第 10 题
基本计数原理★★☆☆☆
How many integers between 1000 and 9999 have four distinct digits?
1000 和 9999 之间有多少个四位数，满足这个数的四个位上数字都不相同？
- A.3024
- B.4536
- C.5040
- D.6480
- E.6561
正确答案 · Correct Answer
B
解析 · Solution
Solution 1
There are 9 choices for the first number, since it cannot be 0, there are only 9 choices left for the second number since it must differ from the first, 8 choices for the third number, since it must differ from the first two, and 7 choices for the fourth number, since it must differ from all three. This means there are integers between 1000 and 9999 with four distinct digits. If you're too lazy to do , we can notice 9×9 = 81 and 8×7=56 The unit digit must be 6. Therefore, the answer is the only answer choice with a unit digit of 6, which is .
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