返回题库

HMMT 二月 2002 · GEN2 赛 · 第 10 题

HMMT February 2002 — GEN2 Round — Problem 10

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. How many four-digit numbers are there in which at least one digit occurs more thanonce? 1
解析

英文解析

  1. 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. 2