In: Advanced Math
There lays a 10x10 square grid in front of Claire and she is instructed to stand in the lower left square of the grid. She is asked to make her way to the top right square of the grid but she can only move 1 square up or 1 square to the right at a time.
1. In how many ways could she make a path to the top right corner?
2. In how many ways could she make a path if she was also required to pass through the center square (5,5)?