HMMT 二月 2002 · GEN2 赛 · 第 10 题
HMMT February 2002 — GEN2 Round — Problem 10
题目详情
- How many four-digit numbers are there in which at least one digit occurs more than once? 1
解析
- How many four-digit numbers are there in which at least one digit occurs more than once? Solution: 4464 . There are 9000 four-digit numbers altogether. If we consider how many four-digit numbers have all their digits distinct, there are 9 choices for the first digit (since we exclude leading zeroes), and then 9 remaining choices for the second digit, then 8 for the third, and 7 for the fourth, for a total of 9 · 9 · 8 · 7 = 4536. Thus the remaining 9000 − 4536 = 4464 numbers have a repeated digit. 2