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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 5, 2021
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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= 757.

 Jul 5, 2021

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