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PUMaC 2017 · 代数（B 组） · 第 2 题

PUMaC 2017 — Algebra (Division B) — Problem 2

专题
Discrete Math / 离散数学
难度
L3
来源
PUMaC

题目详情

  1. Find the coefficient of x y in ( xy + x + 3 y + 3) .
解析
  1. x y = ( xy ) x = ( xy ) x y . ( xy ) x can be formed by choosing 6 xy ’s, 1 x , and 1 3, which can ( )( )( ) 8 2 1 5 2 be done in = 56 ways. ( xy ) x y can be formed by choosing 5 xy s, 2 x ’s, and 1 3 y , 6 1 1 ( )( )( ) 8 3 1 which can be done in = 168 ways. Thus the final coefficient is 56 · 3 + 168 · 3 = 672 . 5 2 1 Problem written by Eric Neyman