Find the number of paths from $A$ to $I,$ if each step must be in a right-ward direction. (For example, one possible path is $A \to B \to C \to E \to F \to H \to I.$)

To count the number of paths from A to I, we can count the number of ways to choose 6 of the 7 letters B, C, D, E, F, G, H. There are (67)=7 ways to do this.