We are given $k$ urns labeled from $1$ to $k$. What is the number of ways to put $n$ indistinguishable balls into the $k$ (distinct) urns, given that each urn has a limited capacity equal to $c$, namely the maximum number of balls that can be put in the same urn?
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Is it suppose to have $c < n$? – Air Mike Feb 15 '21 at 19:10
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From the statement of the problem, $c \leq k$ – true blue anil Feb 15 '21 at 19:12
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@trueblueanil it is not $k.$ It has to be $n$ because $n$ represents the number of balls. Also, even if $c > n$ we could still have a limited capacity for each urn – Air Mike Feb 15 '21 at 19:13
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1The answer to the earlier question to which I linked uses generating functions; you can also use inclusion-exclusion, as noted here. – Brian M. Scott Feb 15 '21 at 19:18