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    Tennis matches

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    A tennis club has 40 members. One afternoon, they get together to play singles matches (one-on-one competitions). Every member of the club plays one match with another member of the club, so twenty matches are held. How many ways can this be arranged?

    The next afternoon, the club members decide to play doubles matches (teams of two pitted against each other). The players are formed into 20 teams, and these teams each play one match each against another team (for a total of ten matches). In how many ways can this be done?

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