2 Questions, I think I got the first one:

a) How many solutions exist to the equation x + y + z = 15, where x, y, and z have to be non-negative integers?

C(17,2) = 136 ... correct?

b) How many solutions exist to the equation xyz = 3^6 * 2 ^ 13, where x, y, and z have to be positive integers?

No idea...