I need to know how to find the number of possible integer solutions to the following problem.
$x_1 + x_2 + x_3 = 0 \text{ where }x_i \ge -5$
Normally, I would do this problem by making it a distribution of identical objects problem by finding the amount of ways to fill each "box" with n different objects. However, I can't do that here (or at least I cannot figure out how to do it here). I know that the answer is
$15+3-1\choose 15$
I understand where the 3 and 1 come from, however, I do not understand where the 15 comes from (my only guess would be $5\cdot 3$, but I'm not sure). Thanks!