How many non-negative integer solutions does this equation have? \[x_1+x_2+\ldots+x_N=n\]

How many non-negative integer solutions does this equation have? \[x_1+x_2+\ldots+x_N=n\]

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Are you considering the solutions to be ordered or unordered? For example, if we wee trying to solve: x + y + z + w = 12 Would the solution (x,y,z,w) = (9,1,1,1) = (1,9,1,1) = (1,1,9,1) = (1,1,1,9) or would that be considered 4 separate solutions? If they are considered the same, then this is a partitions problem, if they are different, then this is a combinations problem.

They are different.

woops!! that's for ... a+b+c+d = N

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