Committee with both sexes

A committee of 44 is chosen from 55 men and 44 women. How many committees contain at least one man and at least one woman?

Show hints (2)+
  1. Count all committees, then subtract the all-men and all-women ones.
  2. (94)(54)(44)\binom{9}{4} - \binom{5}{4} - \binom{4}{4}.

Answer

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120

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Asked at: Timed Mental-Math & Sequences, Game-Based Aptitude

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