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Combinations and Subsets : Probabilities

A committee consists of 8 married couples. In how many ways can a subcommitee of 5 people be chosen so that at most one married couple belongs to the subcommittee?

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The number of ways to choose the 5 people without any limitation is:

C(16,5) = 16!/5! = (16*15*14*13*12)/(5*4*3*2*1) = 4368

The number of ways to choose exactly 2 couples ...

Solution Summary

Combinations and probabilities are investigated.