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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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