1. ## Sets and Probability

I was told to study this problem for an upcoming test, but I'm not confident that I'm doing it right:

"U.S. presidential elections are decided by the Electoral College... Ignoring the number of votes each state has in the Electoral College, but including all possible combinations of states that could be won by either candidate, how many outcomes are possible in the Electoral College if there are two candidates?"

We treat the problem as though there are 51 states (50 states + the District of Columbia).

So 51 states can either be won over by candidate A or candidate B.

I understand that a set of k distinct elements has 2^k subsets. So are there 102 distinct elements (51 states x 2 possible candidates) for this problem? Assuming there are, 2^102 (-1 for the zero set) seems like an awfully large number of combinations.

I'm too tired to think this out properly. Any help would be appreciated.

2. You may be trying too hard in this problem.

I see 2 interpretations. The 1st is the easiest:

Candidate A wins 51 states, Candidate B wins 0.
Candidate A wins 50 states, Candidate B wins 1.
Candidate A wins 49 states, Candidate B wins 2.
etc.
There are 52 possibilities.

The 2nd interpretation is:
Candidate A wins 51 states, Candidate B wins 0.
Candidate A wins 50 states except state 1, Candidate B wins 1 = state 1.
Candidate A wins 50 states except state 2, Candidate B wins 1 = state 2.
etc.
There are 2^51 possibilities here. (Each of 51 states being an A or a B).

3. Thank you for clarifying this for me.