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Fundamental Principle of Counting

Find the numb...

Question

Find the number of rectangles formed on a chessboard:

A

1296

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B

1452

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C

1528

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D

1614

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Solution

The correct option is B 1296
In a chess board there are 8 columns and 8 rows.
Hence the number of rectangles
$= 1^{3} + 2^{3} + 3^{3} + . . . . + 8^{3}$
$= {(\frac{8 \times 9}{2})}^{2} = 1296$

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