+49 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 $(5,7)$?
+128460 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
+49 If i think about it, that should be right. but its not for some reason...
