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Math Help - Multiset

  1. #1
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    Multiset

    Would a question such as:
    How many non-negative integer solutions are there to
    x + y + z = 10?
    be worked out as a multiset question?

    I worked it out like this:
    C(3+10-1,3) = C(12,3) = 220

    Is this correct? If it's incorrect what is the proper way to solve these kinds of questions?
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  2. #2
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    Quote Originally Posted by Lupin View Post
    Would a question such as:
    How many non-negative integer solutions are there to
    x + y + z = 10?
    be worked out as a multiset question?
    I worked it out like this:
    C(3+10-1,3) = C(12,9) = 220
    Is this correct? If it's incorrect what is the proper way to solve these kinds of questions?
    No. It should be \binom{10+3-1}{10}=\binom{10+3-1}{3-1}

    The multiset rule is: To make K selections from N different items is done in \binom{K+N-1}{K}=\binom{K+N-1}{N-1} ways.

    In this problem K=10 & N=3.
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  3. #3
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    Thank you! I got it all figured out now.
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