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→B→C→E→F→H→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.