Find the number of non-negative integer solutions of $x+y+z=14$ given that $0 \leq x,y,z \leq 9$
I know that similar questions have been answered before. Anyway, this can be solved using generating sequences or using star and bar argument along with PIE.
My question is a bit different. I feel like this can also be somehow manipulated and solved with the help of a dummy variable. Please help me with that, if that's possible.