HMMT 二月 2002 · 冲刺赛 · 第 28 题

英文解析

28. Count how many 8-digit numbers there are that contain exactly four nines as digits.
    ( )
    Solution: There are · 9 sequences of 8 numbers with exactly four nines. A sequence 48
    of digits of length 8 is not an 8-digit number, however, if and only if the first digit is 4
    ( )
    zero. There are 9 8-digit sequences that are not 8-digit numbers. The answer is thus 37
    ( ) ( )4
    8 7
    4 3
    · 9 − 9 = 433755 .
    4 4