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Possible Duplicate:
How many ways can $b$ balls be distributed in $c$ containers with no more than $n$ balls in any given container?

There are $k$ balls and $d$ bowls. In how many ways the balls can be put in the bowls? Capacity of bowls is limited, each bowl can contain $\{0,1,2,\dots,M\}$ balls.

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    Is this homework?2012-08-17
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    So each bowl is larger than some other bowl (sans the 0 bowl) meaning there are M bowls total? Also, does the order in which the n balls are put in matter? Is each ball unique? Do the balls entirely fill each bowl?2012-08-17
  • 0
    [This earlier answer](http://math.stackexchange.com/a/120327/12042) gives the reasoning in considerable detail.2012-08-17
  • 0
    I think the question might have been cross-posted on Mathematics and CrossValidation and the stats moderators migrated their's to here giving us a duplicate.2012-08-17

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