Discussion
Given a group of \(n\) married women and their \(n\) husbands at least how many people be chosen from this group of \(2n\) people to guarantee the set contains a married couple ?
Answer: C
At least \(n + 1\) people must be chosen.
Think of the \(n\) couples as \(n\) pigeonholes. With \(n + 1\) people chosen, two of them must belong to the same couple, by the pigeonhole principle, so a married couple is guaranteed.
With only \(n\) people this can fail: choose all \(n\) wives (or one person from each couple) and no couple appears. So \(n\), and certainly \(n - 1\), are not enough, and \(n + 2\) is more than necessary.
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