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

Answer:

The number of ways to get from (0, 0) to (5, 7) moving in this manner is given by :

(7 + 5) ! / (7! 5!) = 12! / (7! 5! )  = 792 ways

From this, we want to subtract the ways to get from (0, 0) to (2, 3)

This is given by  

(3 + 2)! / (3! 2!) = 5! / (3! 2!) =  10 ways

So 792 - 10  = 782 routes

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