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HMMT 二月 2000 · POW 赛 · 第 13 题

HMMT February 2000 — POW Round — Problem 13

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. Find the number of "w ords" of length m from a set of n letters, if each letter m usto ur at least on e in each w ord.
解析

英文解析

  1. This is the sum of all the distribution n um b ers in which the n um b ers m : : : m run
    1 nm !Pm + ::: m = m
    1 nthrough all p ossible sequen es of n p ositiv e in tegers adding up to m :
    m > =1
    m ! m ! ::: m !
    1 2 ni