+0  
 
+2
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avatar+29 

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 $(5,7)$?

 Jun 21, 2021
 #1
avatar+120930 
+3

Number of paths  ftom  (0, 0)  that  pass through  ( 4,3)  =

 

(R  R  R  R   U  U  U)  =   C( 7,4)  = C(7, 3)  =   35

 

Number of paths  from (0,0)  to  ( 5,7) =    

 

(R R R R R  U U U U U U U )  =   C(12, 5)  = C(12,7)  =  792

 

So....total  paths  from   (0, 0)  to (5,7)  that do not pass through  (4,3)  =  792   -  35  =    757

 

 

 

cool cool cool 

 Jun 21, 2021
 #2
avatar+29 
+2

If i think about it, that should be right. but its not for some reason...

 Jun 21, 2021

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