The members of City Council are to vote yes or no on each of seven issues. In marking a ballot, each councilor has the option of abstaining on as many as six of the issues, but should not abstain in all seven cases. In how many ways can the ballot be marked?

Question

The members of City Council are to vote yes or no on each of seven issues.  In marking a ballot, each councilor has the option of abstaining on as many as six of the issues, but should not abstain in all seven cases. In how many ways can the ballot be marked?

drwls · Accepted Answer

3^7 - 1 = 2186 There are 3^7 possible choices of Y,N, and A in seven ballots, but one of them (seven A's) is disallowed.

Anonymous · Answer

what is the A for?

kitkat · Answer

I do not get the 3^7 wouldn't it be 7^3 because you have seven questions but can can choose to do one of three for each question?