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Problem : How many ways are there to make $n$ by adding $k$ non-negative integers, where order matters. Suppose $n=4$ and $k=3$. There are 15 solutions using $0, 1, 2, 3, 4$:
$(0,0,4), (0,1,3), (0,2,2), (0, 3, 1), (0, 4, 0), (1, 0, 3), (1, 1, 2), (1, 2, 1), (1, 3, 0), (2, 0, 2), (2, 1, 1), (2, 2...