How many ways are there to select 10 donuts with 5 different flavors? Note that it is not necessary to include all 5 flavors in 1 selection. Write your answer as the coefficient of $x^n$ (for some $n$) of a power series in rational form. Each selection of donuts are different from the rest.
Please help :(
Hint: Consider $f_i$ the number of donuts of flavor $i$, for $i=1,\ldots,5$. So you have to determine the number of solutions of $f_1+f_2+f_3+f_4+f_5=10$, with $0\leq f_i\leq 10$.