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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 $(5,7)$?

 Jul 7, 2021
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The number of ways is c(12,5) - c(7,2)*c(5,2) = 582.

 Jul 7, 2021

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