framing of a recursive solution

http://ift.tt/28Q8Wm4 I found this practice question on hackerearth. I think this has some recursive solution to it but not able to exactly frame it up.

I could find that there are four possibilities at each step.

1. both A and B selected

2. None selected

3. A selected and B not selected

4. B selected and A not selected

so plzz could you help in writing a solution to this question