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Math Help - Combinatorics Question

  1. #1
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    Combinatorics Question

    In how many ways can I package 6 colors of posterboard in packages of 5 posterboards each ?
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  2. #2
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    Hello, fholik!

    In how many ways can I package 6 colors of posterboard in packages of 5 posterboards each?

    Assuming that the order of the colors in a package does not matter,
    . . we are choosing 5 colors from the available 6 colors.

    There are: . _6C_5 \:=\:{6\choose6} \:=\:6 ways.

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  3. #3
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    Combinatorics Question

    I misstated the original problem. If you have an endless supply of posterboard in 6 different colors, in how many ways can you package 5 posterboards ?
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  4. #4
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    Quote Originally Posted by fholik View Post
    I misstated the original problem. If you have an endless supply of posterboard in 6 different colors, in how many ways can you package 5 posterboards ?
    If the first answer is not what you meant, then I assume that a package could contain say three yellow, one green and one red.
    If that is the case this is a multi-selection problem.
    We can select K items from N different kinds in \binom{K+N-1}{K} ways.
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  5. #5
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    Combinatorics Question

    That is the solution I was looking for. Thank you. fholik
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