AMC 8 2009 Problem 16

AMC8 2009 年第 16 题

基本计数原理★★★☆☆

How many 3 -digit positive integers have digits whose product equals 24 ?

有多少个 3 位正整数，满足各个位上数字之积是 24？

正确答案 · Correct Answer

解析 · Solution

Solution 1

With the digits listed from least to greatest, the 3 -digit integers are 138,146,226,234. 226 can be arranged in

\displaystyle \frac{3!}{2!} = 3

ways, and the other three can be arranged in 3!=6 ways. There are 3+6(3) = 21 3-digit positive integers.

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