Question

Marvin the fly starts at $(0,0).$ Each step, Marvin moves one unit right or one unit up. He is trying to get to the point $(5,7)$. However, at $(4,3)$ there is a frog that will eat him if he goes through that point. In how many ways can Marvin reach $(5,7)$?

Answer 1

You probably have a formula f(x,y) for getting from (0,0) to (x,y).
Seems like this would be f(5,7) - f(4,3) - f(5-4,7-3)
That is, throw away all the paths that lead to (4,3), and then throw away all the paths that would lead from (4,3) to (5,7)

Answer 2

I need help on this

Answer 3

Could anyone post the answer? I would like to check my work. Thanks in advance!