Hi.

I am having some difficulty with this inclusion-exclusion problem, and I would love some help.

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Determine the number of integer solutions to X1 + X2 + X3 + X4 = 19, where -5 ≤ Xi ≤ 10, for all 1 ≤ i ≤ 4.

What I have done is create another equation to solve, since we already know how to solve non-negative integer solutions, C(n + r - 1, r), but I don't know whether I have done this step right.

Let Y1 + Y2 + Y3 + Y4 = 24, where Xi ≤ 15, Yi = Xi + 5 for all 1 ≤ i ≤ 4. IS THIS RIGHT?

If this is right, I am pretty sure I know how to go on from here, but I am unsure of this particular step.

Thanks in advance