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    OlympiadMediumCombinatorics7–9

    In how many ways can 66 people be split into 33 pairs? (The pairs are not labelled.)

    De quantas maneiras se podem dividir 66 pessoas em 33 pares? (Os pares não são identificados.)

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    Solution

    Line the six up in 6!6! ways and read off three pairs. Each pair may be written in 22 orders and the three pairs in 3!3! orders: 72023×6=15\frac{720}{2^{3} \times 6} = 15.