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Math Help - Prom Possibilities

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    Prom Possibilities

    9 boys and 6 girls are going to prom together. How many different ways are there to arrange them into six boy-girl couples? (Assume the remaining three boys don't mind going stag.)

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    Quote Originally Posted by Mr_Green View Post
    9 boys and 6 girls are going to prom together. How many different ways are there to arrange them into six boy-girl couples? (Assume the remaining three boys don't mind going stag.)

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    Pairing 6 boys with three girls is represented by the following Combinations with the format nCr:

    15C6 x 15C6 = 3003^2 = 9,018,009 ways to arrange six boy-girl couples.
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    wow. that's a lot of possibilities..aha
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    Quote Originally Posted by Mr_Green View Post
    wow. that's a lot of possibilities..aha
    In fact, it is too many! It is a gross overcounting.
    This is a permutation of nine choosing 6: P(9,6)=60480.

    Suppose we have the girls: Ann, Bee, Cat, Dot, Eliz, and Fran.
    We have 9 choices for Ann; 8 choices for Bee; 7 choices for Cat, …, 4 choices for Fran.
    Last edited by Plato; February 28th 2007 at 03:13 PM.
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