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 $(5,7)$?

Guest Mar 3, 2021

#1**0 **

there are 12 choose 5 = 792 possible ways of getting to point (5,7) from (0,0), and there are 7 choose 3=35 possible ways of getting to point (4,3) from (0,0), so the number of ways to get to (5,7) from (0,0) are

792-35=$\boxed{757}$

SparklingWater2 Mar 3, 2021