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Math Help - partitioning/multinomial coefficients

  1. #1
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    partitioning/multinomial coefficients

    The following problem is from my probability and statistics book:

    A fraternity consisting of 30 members wants to play "seven versus seven" flag football. How many different match-ups are possible?

    This question is asked after the partitioning/multinomial coefficients section so I know there must be a solution using this method. I thought it was simple:

    30! / (7! * 7! * 16!) = 4.9909.. * 10^11
    or:
    30C7 * 23C7 = 4.9909.. * 10^11

    however the solution in the back of the book is 2.495*10^11

    I cannot figure out how they got this answer. Does anybody else have any ideas?

    Thank you for your time!
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  2. #2
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    Quote Originally Posted by probstud View Post
    The following problem is from my probability and statistics book:

    A fraternity consisting of 30 members wants to play "seven versus seven" flag football. How many different match-ups are possible?

    This question is asked after the partitioning/multinomial coefficients section so I know there must be a solution using this method. I thought it was simple:

    30! / (7! * 7! * 16!) = 4.9909.. * 10^11
    or:
    30C7 * 23C7 = 4.9909.. * 10^11

    however the solution in the back of the book is 2.495*10^11
    \dfrac{\mathcal{C}(30,7)\cdot\mathca{C}(23,7)}{2}=  249545310300.
    Divide by two to account for symmetry.
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