Number if rectangles on a chess board is

In a chess board there are sixty four square boxes. So, there are nine parallel lines in one direction and nine parallel nines in a perpendicular direction. Each selection of a pair of line from first set and a pair of lines form the second set gives us a rectangle.

$\therefore$  Number of rectangles $={}^9{\text{C}}_{\text{2}}{\times }^9{\text{C}}_{\text{2}}$