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How many different rectangles with sides parallel to the grid can be formed by connecting four of the dots in a 5*5 square array of dots, as in the figure below?

 

(Two rectangles are different if they do not share all four vertices.)

 

 Dec 31, 2021
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Hello Guest!

A rectangle can be made with 2 vertical dots and 2 horizontals.

For the 2 vertical dots there are 5 to choose from. 

that is choosing 2 dots from 5 or 5 choose 2. 

Now applying the same logic, we also need to choose 2 horizontal dots.

There are 5 dots to choose from. so we have 5 choose 2 

5 choose 2 is 10. there are 10 choices for horizontal and 10 choices for vertical.  10x10=100 choices for a rectangle

 Jan 1, 2022

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