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).