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Math Help - probability

  1. #1
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    probability

    how many different teams of 9 can be made from 22 football players?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Help09 View Post
    how many different teams of 9 can be made from 22 football players?
    C^{22}_9=\frac{22!}{9!(22-9)!}<br />

    To see this consider the players choosen in turn, the first can be any of the 22, the second any of the remaininr 21, and so on.

    So the number of ways the team can be choosen in sequence is:

    22 \times 21 \times ... \times (22-8) = \frac{22!}{(22-9)!}

    but this overcounts the number or ways as every permutation of every
    team of 9 appears in this process, so we have to divide by the number
    of permutations of a team of 9 players (which is 9!), which gives the result.

    RonL
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