This is a question in GregMAT’s quant practice.

Starting from point (0,0) on the xy-coordinate plane, what is the number of distinct routes to point (5,7) that can be drawn if each route must pass through point (2,4) and only perpendicular up and right movements of distance 1 are allowed for each leg of the route?

**I’m wondering how would you solve this problem if:**

- perpendicular up, down, right and left movements of distance 1 were allowed?
- movements of distance 2 were allowed?