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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 $(2,2)$.  However, at $(1,1)$ there is a frog that will eat him if he goes through that point.  In how many ways can Marvin reach $(2,2)$?

 Dec 21, 2023
 #1
avatar+126665 
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The ways to get to  (1,1)  from (0,0)  =  C(2,1)  = 2

 

Ways to get to *2,2) from (0,0) =    C(4,2)  = 6

 

So .....ways to  get from  (2,2) from (0,0)  without going through (1,1) =  6 - 2 =  4

 

 

cool cool cool

 Dec 21, 2023

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