Hi all. I have a grid with 4 points, A, B, C, and D. Each valid move is either going to the right for one block or going down for 1 block. Here is the grid. I need to calculate the following: a) How many different valid routes from A to D? b) How many valid routes from A to D that must avoid B? c) How many valid routes from A to D that must pass through Both B and C? d) How many valid routes from A to D that must pass through B but must avoid C ? I believe for A, I would calculate 13 choose 9 to obtain 715 possible routes. Where I am confused is how I calculate in the avoidance and musts. For example, on b, if I wanted to avoid B, would I treat A to be like a mini 4x5 sub-grid? Would I subtract 4 choose 4 from 715 to obtain 710 possible routes? Any help is appreciated. I can't seem to find any information on this in my book :(.