This is from my textbook, which has no solutions for any of the problems (bad).
Determine the generating series for the number of 5-combinations where M, A, T, H in which M and A can appear any number of times but T and H can appear at most once.
Can I just treat this as a Cartesian product of quantities of M, A, T, and H respectively and give a generating function with respect to sum as
$$\Phi_S(x)=(1+x+x^ 2+\cdots)^2(1+x)^ 2$$?
Looks right to me. The number of 5-combinations is the coefficient of x^5, but I suppose you know that already. I'm assuming the order of the letters is irrelevant.