how many combinations of positions residents could mark

Ballots for municipal elections usually list candidates for several different poisitions. If a resident can vote for a mayor, two councillors, a school trustee, and a hydro commissioner, how many combinations of positions could the resident choose to mark on the ballot.

I was wondering what the difference between doing 2^n-1 is, and (1+1)(2+1)(1+1)(1+1)-1 is.

Because I tried (1+1)(2+1)(1+1)(1+1)-1 first, but got the wrong answer so I then did 2^5-1 and got the right answer.

How do you know which to use,and whats each for then?
Thanks.

Assuming that a voter must vote for at least one position then \(\displaystyle 2^5 - 1\) is the correct answer. If you have a set of five elements then there are \(\displaystyle 2^5\) subsets of that set. But one of those subsets is empty, no selection, so we subtract 1.

oh yea thanks, i found out today the back of the book was wrong