HMMT 二月 2002 · ADV 赛 · 第 3 题

英文解析

3. How many four-digit numbers are there in which at least one digit occurs more thanonce?
   Solution: 4464 . There are 9000 four-digit numbers altogether. If we consider howmany 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.