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  4. The number of rectangles which we can form on a chess board is

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Q. The number of rectangles which we can form on a chess board is

Permutations and Combinations

Solution:

There ate 9 horizontal and 9 vertical lines on a chess board. To from a rectangle we require two horizontal and two vertical lines. Thus the no. of rectangles on the chess board
$=\,{}^{9}C_{2} \times \,{}^{9}C_{2}=36 \times 36$
$=1296$.