THE CHESSBOARD PROBLEM

Probability Level 3

How many rectangles are there in a 20*14 chess board?


The answer is 22050.

Seemanta Bhattacharjee by Seemanta Bhattacharjee , 23, Bangladesh

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2 solutions

In a 20*14 chessboard, there are 21 horizontal lines and 15 vertical lines.To make a rectangle, we have to choose 2 lines out of 21 and then 2 lines out of 15. Hence there are (21 C 2)(15 C 2)= 22050 rectangles that can be formed.

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Stop copying JOMO 7 problems. At least credit them if you do so.

mathh mathh - 6 years, 10 months ago

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Hope u r satisfied with the set JOMO 7 PROBLEMS.

Seemanta Bhattacharjee - 6 years, 10 months ago

Of course. I just wanted to share them with my friends at BRILLIANT.

Seemanta Bhattacharjee - 6 years, 10 months ago

solved similarly

PUSHPESH KUMAR - 6 years, 8 months ago
Parth Lohomi
Sep 12, 2014

here is the formula for calculating the number of rectangles of a (m*n) chess board

{[m(m+1)]/2}{[n(n+1)/2]}

putting value of m and n we get 210 x 105 = 22050

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