Question

Find the total number of rectangles present in a $8\times 8$ Chessboard

• A. 64
• B. 1024
• C. 1296
• D. 2048

Answer 1

The correct option is C 1296

The total no. of vertical lines present in the first row = 9.
Total no. of ways in which 2 lines can be chosen from 9 lines = 9C2.
Similarly, the total no. of horizontal lines present in the first column = 9.
Total no. of ways in which 2 lines can be chosen from 9 lines = 9C2.
Thus, the total no. of rectangles that could be formed $=9C2\times 9C2.=\frac{\left(\right(9\times 8)}{(1\times 2))}\times \frac{\left(\right(9\times 8)}{(1\times 2))}=36\times 36=1296$