This problem was asked by Facebook.
There is an N by M matrix of zeroes. Given N and M, write a function to count the number of ways of starting at the top-left corner and getting to the bottom-right corner. You can only move right or down.
For example, given a 2 by 2 matrix, you should return 2, since there are two ways to get to the bottom-right:
- Right, then down
- Down, then right
Given a 5 by 5 matrix, there are 70 ways to get to the bottom-right.