Question

Determine the number of rectangles that can be formed on a chess-board.

Answer 1

We know that ,

The no. of rows and columns in a chase board $8\times 8$

Number of ways to select $1$ grid from a column $=8$

Now, I can select $1,2,3,4,5,6,7$and $8$ adjacent grid from the row to from a square $8\times 8$.

Hence, number of ways selecting this way $=8(1+2+3+4+5+6+7+8)$.

Then,

Total number of ways $=8(1+2+3+......8)+7(1+2+3+.....8)+6(1+2+3+.....8)+...............+1(1+2+3+.....8)$

$=(1+2+3+4+5+6+7+8)(1+2+3+4+5+6+7+8)$

$=36\times 36$

$=1296$

Hence, this is the required number of ways.