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$x_1,x_2,...,x_n$ are integer numbers in the range [0,B-1]. Count the number of solution for $x_1+x_2+...+x_n=k$.

I know this problem is similar to the one here Number of ways of partitioning a sum into ordered non-negative summands

But now there is constraint on the range of $x_i$. In the problem text it gives a hint to use principle of inclusion and exclusion. Does anyone have a clue?

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Hai Phan
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  • @BrianM.Scott I don't see how the first question you linked is related, but the second is essentially the same, so I'll vote to close. – tomasz May 17 '13 at 20:49
  • @tomasz: They’re all three essentially the same question: how many solutions in non-negative integers are there to $\sum_{k=1}^mx_k=n$ subject to the constraint that each $x_k\le b$? – Brian M. Scott May 17 '13 at 20:53
  • @BrianM.Scott: I see now. You're right. :) – tomasz May 17 '13 at 21:45

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