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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 his home at (4,6).  However, at (2,4) here is a frog that will eat him if he goes through that point.  In how many ways can Marvin reach his home?

 Dec 9, 2022
 #1
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Basically, we have a lattice grid. There total number of ways to get from the Origin to (4, 6) is 10 choose 4 = 210. The total number of ways to get from (0,0) to (2, 4) is 6 choose 2, and from (2, 4) to (4, 6) is 4 choose 2. 6 choose 2 * 4 choose 2 = 90. Subtracting, the total number of ways marvin can reach his home is 210 - 90 = 120 ways.

 Dec 9, 2022

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