Mack the bug starts at (0,0) at noon and each minute moves one unit right or one unit up. he is trying to get to the point (5,7). however, at (2,3) there is a spider that will eat him if he goes through that point. in how many ways can mack reach (5,7) ?

This is a very nice counting question. Suggestion / Hint: Count how many ways he can get from (0,0) to (5,7) by going through the point (2,3). Then subtract that from ALL POSSIBLE ways he can get from (0,0) to (5,7). Hint for the hint: How many ways he can get from (0,0) to (5,7) by going through the point (2,3)? Well, that's the SUM of how many ways he can get from (0,0) to (2,3) and how many ways he get get from (2,3) to (5,7). Hope this helps! :)