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HMMT 二月 2000 · POW 赛 · 第 13 题

HMMT February 2000 — POW Round — Problem 13

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. Find the n um b er of "w ords" of length m from a set of n letters, if ea h letter m ust o ur at least on e in ea h w ord.
解析
  1. This is the sum of all the distribution n um b ers in whi h the n um b ers m : : : m run 1 n P m ! m + ::: m = m 1 n through all p ossible sequen es of n p ositiv e in tegers adding up to m : m > =1 m ! m ! ::: m ! i 1 2 n