Use generating functions to determine the number of ways to distribute 10 Kit-Kat bars and 15 Mr. Big bars to four different people, so that no person receives more than five of each bar.
Answer: I am at a loss given that there are two different groups of chocolate bars. Do I create a generating function for each type of bar and multiply them together?
Use a bivariate generating function, with the monomial $x^n y^k$ tracking the number of ways to distribute $n$ of one bar and $k$ of the other: $$(1+x+x^2+x^3+x^4+x^5)^4 (1+y+y^2+y^3+y^4+y^5)^4$$ You want the coefficient of $x^{10} y^{15}$.
Equivalently, multiply the coefficients of $x^{10}$ and $x^{15}$ in $$(1+x+x^2+x^3+x^4+x^5)^4$$