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Number of rectangles in MxN matrix

(1 votes, average: 5.00 out of 5)

May 25, 2014 by puzzler 1 Comment

How many number of rectangles are present in a MxN matrix?


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Out of four points of a rectangle, two points should be in one row and other two points should be in other row. If you select any two points in the top row then we dont have any choice for two points in the bottom row, there is only one possibility for that, as in the image below.

Number of rectangles in MxN matrix

Number of rectangles in MxN matrix

So we first select any two rows and then select any two points in columns.
Number of ways to select any two rows = mP2
Number of ways to select any two points in a row = nP2
Thus total number of rectangles possible are = mP2*nP2

Here nPk = n!/(n-k)!

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Comments

  1. Nitin Jain says

    September 20, 2014 at 12:49 pm

    Answer would be:
    m*n*(m+1)*(n+1)/4
    i.e sum of all number from 1 to M * sum of all number from 1 to N

    Reply

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