Moving only south and east along the line segments, how many paths are tehre from A to B? If you can explain using combinaations and permutations, it would be AWESOME! TANKS SO MUCH!!!

please help, i have to teach my brother how to do this after. thanks

There are C(9,3) = 84 paths, but you have to subtract 2 because of the two missing segments. That leads to 84 - 2 = 82 paths.