How can I find the minimum number of open rectangles in a grid?

The number of rectangles that you can find on chess board is = ? permitutation ?

• A= 1196 B=1096 C=1296 D=1000 please explain it because i am in learning stage.

• Answer:

  you need to find out the # of distinct rectangles (incl. squares, since squares are a spl. type of rectangle) in a chessboard with 64 squares if you observe carefully, to form the chessboard, you require NINE lines horizontally & NINE lines vertically. and if we combine any 2 points on a horizontal line with any 2 on vertically matching lines, we shall get a rectangle, thus # of rectangles = 9C2 * 9C2 = [(9!/(2!*7!)]^2 = 1296 [ C ] <--------