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Unique ways to keep N balls into K Boxes?

Number of ways to put N items into K bins with at least 1 per bin?

I know that normally you can do N + K + 1 choose K - 1 or something like that, but that allows for bins where nothing is placed inside. What about when there must be at least 1 item per bin?

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    Are the items indistinguishable and the boxes distinguishable? Are they both indistinguishable? Both distinguishable?2012-07-10
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    @ArturoMagidin: I'm not sure... 7 and 3 yield 4, so I think order does not matter on both counts (all indistinguishable)2012-07-11

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