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Math Help - s identical objects in n identical boxes - how many ways?

  1. #1
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    s identical objects in n identical boxes - how many ways?

    Hi, could someone help me with this problem - suppose I have s identical balls that I want to put in n identical boxes - in how many different way can I do this?

    For example: s=3, n=3:

    |ooo|||
    |oo|o||
    |o|o|o|

    So the answer is 3.

    s=6, n=2:

    |oooooo||
    |ooooo|o|
    |oooo|oo|
    |ooo|ooo|

    So the answer is 4.

    It's easy to do it ad hoc, but the general principle escapes me.

    Thanks!
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  2. #2
    Member Traveller's Avatar
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    There is a recurrence relation, but no compact formula has been found yet.

    Partition (number theory) - Wikipedia, the free encyclopedia
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  3. #3
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    Bummer, I was hoping that there was an elegant solution to this problem. Thanks!
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  4. #4
    MHF Contributor undefined's Avatar
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    I'm not sure if the Wikipedia page has the recurrence the OP is after. We can sum the function P(n, k) given here

    Partition Function P -- from Wolfram MathWorld

    after equation (54) from 1 to k. Also, it's mentioned here, lower left cell

    http://www.johndcook.com/TwelvefoldWay.pdf
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