AMC 8 2009 Problem 13
AMC8 2009 年第 13 题
概率★★★☆☆
A three-digit integer contains one of each of the digits 1 , 3 , and 5 . What is the probability that the integer is divisible by 5 ?
一个三位整数包含了数字 1，3 和 5，且每个出现一次。那么这个整数能被 5 整除的概率是多少？
- A.
- B.
- C.
- D.
- E.
正确答案 · Correct Answer
B
解析 · Solution
Solution 1
The three digit numbers are 135,153,351,315,513,531. The numbers that end in 5 are divisible are 5, and the probability of choosing those numbers is .
The number is divisible by 5 if and only if the number ends in 5 (also 0, but that case can be ignored, as none of the digits are 0 ) If we randomly arrange the three digits, the probability of the last digit being 5 is .
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