In part (e) The path A-X-N-B cannot be considered as shortest path. since after reaching X we have to go one step back horizontally to reach N. so, path A-X-N-B is taking a step more than the path A-N-X-B. Please correct me if I am wrong. Reply
CAT-holics 
I think there is a mistake in part b question.
Please elucidate? What’s the mistake?
regards
J
Isn’t it the number of ways from A to X and X to B are 7C2 and 6C3 ways respectively ?
Sorry, My mistake. I was looking at A to X and X to B instead of P to X and X to Q.
A mistake in part d, i guess
In part (e)
The path A-X-N-B cannot be considered as shortest path. since after reaching X we have to go one step back horizontally to reach N. so, path A-X-N-B is taking a step more than the path A-N-X-B.
Please correct me if I am wrong.
Sorry I got it . No need to explain.