Let n be a positive integer. Each point (x, y) in the plane, where x
and y are non-negative integers with x + y < n, is colored red or blue, subject to the following condition:
- If a point (x, y) is red, then so are all points (x', y') with x' ≤ x and y' ≤ y.
Let A be the number of ways to choose n blue points with distinct x-coordinates, and let B be the number of ways to choose n blue points
with distinct y-coordinates. Prove that A = B.