2017 AMC 8 第 20 题
先试着解答 2017 AMC 8 第 20 题，然后核对你的答案与视频与精心整理的解答，解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2017 AMC 8 解答，或核对答案。
所有题目均经美国数学协会（MAA）官方合法授权使用。
20.
从 到 （含端点）之间随机选一个整数。它是奇数且各位数字互不相同的概率是多少？
An integer between and inclusive, is chosen at random. What is the probability that it is an odd integer whose digits are all distinct?
小提示：
直接统计符合条件的四位数，再除以四位整数总数
Count favorable four-digit numbers directly, then divide by the number of four-digit integers.
大提示：
先选奇数个位，再选非零千位，再选剩余两个数字
Choose the odd units digit first, then choose the nonzero thousands digit, then the remaining two digits.
视频讲解：
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文字解答：
这个数是奇数，所以个位数字有 种选择。千位数字不能为零，也不能等于个位数字，因此有 种选择。百位有 种选择，十位有 种选择。符合条件的数共有 ，所以概率为 。
所以正确答案是 B。
Since the number is odd, the last digit is odd, giving possibilities. The thousands digit cannot be zero or the number we already got, so that gives possibilities. Similarly, the hundreds digit has possibilities, and the tens digit has possibilities. This gives a total of making the probability
Thus, B is the correct answer.
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