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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 27, 2020
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We can use complementary counting.  There are 12/(5!*7!) = 792 paths to (5,7).  You must subtract 7!/(4!*3!) = 35 paths, so there are 792 - 35 = 757 good paths.

 
 Jul 27, 2020

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