I've just managed to stump myself. Lets say you have(adsbygoogle = window.adsbygoogle || []).push({});

M (identical) marbles and N boxes. How many ways

can you put the marbles in the boxes if each box

can have at most k (k <= M) marbles?

for k=M we can take M .'s to be the marbles

and N-1 |'s to be the boxes so a valid configuration

is a sequence like ..|.|...||.. so we end up with

(M+N-1) choose M.

for k=1, we must have M<N, and

we have N choices for the first marble,

N-1 choices for the second, ...

which is just N choose M possibilities.

is there a formula for arbitrary k?

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# Tough combinatorics problem

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