Jamboree way

If we choose any two horizontal lines and any two vertical lines the enclosed quadrilateral formed will be a rectangle.
The given figure has 5 horizontal lines and 6 vertical lines.
The number of ways we can select 2 horizontal lines out of 5 horizontal lines = 5C2 = 10
The number of ways we can select 2 vertical lines out of 6 vertical lines = 6C2 = 15

Total number of rectangles formed = (The number of ways we can select 2 horizontal lines) x (The number of ways we can select 2 vertical lines)

Total number of rectangles formed = 10 x 15 = 150
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Aryama Dutta Saikia
Jamboree Education Pvt. Ltd.

Hi, Can you please share your approach. Though my answer is correct, I do not consider my way to be reliable in the long run.

Hi,
I think you require to change your answer as jamboree way, which is also the normal way, is correct but seems to be answering some other Q....

there is a grid of 6 by 5 and not 4 by 3..
for a rectangle we can choose 2 horizontal points and 2 vertical points...
total ways = 6C2 * 5C2=15*10=150
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For a rectangle we need two horizontal lines out of 5 and we need 2 vertical lines out of 6

= 6C2*5C2 = 15*10 = 150

Answer: option D
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You are right. The solution presented includes square as well. The formulae is blindly applied to include squares.
To prove, we can solve a simple combination.

Let's take a 2X3 rectangle grid made up of small squares.
Applying the same logic, it will be 3C2 X 4C2 = 3*6 = 18. This will include squares as well.

There are only 10 such rectangles which can be formed here.
rectangles with 1x2 = 2 per row = 4 in total
rectangles with 2x1 = 1 per column = 3 in total
rectangles with 1x3 = 1 per row = 2 in total
rectangle with 2x3 = 1 in total

Moreover, there are 8 such squares in total
squares 1x1 = 2*3 = 6
squares 2x2 = 1*2 = 2

Now, applying the same to the question.
Total quadrilaterals that can be formed is 5C2 * 6C2 = 10*15 = 150.
The number of squares in this will include = 4*5 + 3*4 + 2*3 + 1*2 = 40
Hence, the total number of rectangles will be 150 - 40 = 110

With respect to the question, I suppose (looking at the picture), the smaller units appear to be rectangle. Hence, the question was incorrectly worded as 20 equal squares instead of 20 equal rectangles. If it is the latter, 150 is right.