HMMT 二月 2002 · 冲刺赛 · 第 28 题
HMMT February 2002 — Guts Round — Problem 28
题目详情
- [6] Count how many 8-digit numbers there are that contain exactly four nines as digits.
解析
- Count how many 8-digit numbers there are that contain exactly four nines as digits. ( ) 8 4 Solution: There are · 9 sequences of 8 numbers with exactly four nines. A sequence 4 of digits of length 8 is not an 8-digit number, however, if and only if the first digit is ( ) 7 3 zero. There are 9 8-digit sequences that are not 8-digit numbers. The answer is thus 4 ( ) ( ) 8 7 4 3 · 9 − 9 = 433755 . 4 4