This is from my textbook which does not give solutions to problems (i.e. not homework).
Find the generating series for the number of election results involving 4 candidates with respect to the number of voters.
This is easy and is obviously $(1+x+x^2+\cdots)^4$. However, the next question is hard:
Do the same, except assume that all 4 candidates vote for themselves.
How would I solve this problem then?
In the first question, each of the four candidates can have $0$ or more people who vote for them. In the second question, each candidate is guaranteed at least $1$ vote (themselves). Hence, we obtain: $$ (x + x^2 + x^3 + \cdots)^4 $$