How to find the number of rectangles (not squares) in this mathematical iq test within small time limit?

Question

Answer 1

In order to construct a rectangle we must select 2 horizontal sides and 2 vertical sides.

In an M by N grid there are M + 1 horizontal sides and N + 1 vertical sides.

The total number of rectangles is the number of ways to choose 2 horizontal sides from M + 1 times the number of ways to choose 2 vertical sides from N + 1.

The number of ways to choose k elements from n total elements is called n choose k in combinatorics and written like n!/((n-k)!k!), where ! denotes the factorial operation.

Thus the total number of rectangles in a 4 x 4 grid is [5!/(3!2!)]² = (5*4/2)² = (10)² = 100.