In this problem we want to count the paths that go from point A to point B in the following diagram, moving along the lines and in each step moving either one unit down or one unit to the right. In the picture the boxes should be evenly spaced. 1.) The number of paths is___________________ 2.) How many paths are there that include no two consecutive downward move? 3.) How many paths are there that do not enter the orange region? For number one I was thinking that there are 10 different paths we could take and at most we could only take 4 so i'm thinking it 10C4. For number 2 I was thinking that it is going to be something like 4C3 or 5C3 but im not sure. For number 3 I decided to break it up into the shaded region and the none shaded region. For the none shaded region I think there is 7C3 paths and for the shaded I think there (8C4)/2. I don't think that is right because 7C3 +8C4 does not equal 10C4 that I said for one. Any help would be greatly appreciated.