Question

The number of rectangles excluding squares from a rectangle of size 9 x 6 is

• A. 391
• B. 791
• C. 842
• D. 250

Answer 1

The correct option is B 791

If you are given a grid of size $9\times 6$ then number of rectangles means you have to choose two horizontal lines and two verticle lines from all the line.

So total number of vertical and horizontal lines are $7$ and $10$ respectively

So total number of rectangle are $10C_2\times 7C_2$ $=945$

Number of Squares are $=9\times 6+8\times 5+7\times 4+6\times 3+5\times 2+4\times 1=54+40+28+18+10+4=154$

So number of rectangles are $945-154=791$