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How many parallelograms are formed when a set

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How many parallelograms are formed when a set [#permalink] New post 12 Sep 2018, 22:47
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How many parallelograms are formed when a set of five parallel lines intersect another set of four parallel lines ?

A) 120

B) 60

C) 36

D) 20

E) 10

can anyone please put solution for this.
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Re: How many parallelograms are formed when a set [#permalink] New post 13 Sep 2018, 12:17
I don't think there's any mathematical formula that can help you (at least directly) on this. You'll just have to sketch it and then count by hand.


What you could do is first take the 12 smallest parallelograms, then take 2 of them to count as one, then 3 of them to count as one and so on. In the end, you'll take the whole quadrilateral as one parallelogram.

However, you should keep in mind that the smaller parallelograms you are combining are actually combined into parallelograms and not into any other shapes.
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Re: How many parallelograms are formed when a set [#permalink] New post 13 Sep 2018, 19:06
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AchyuthReddy wrote:
How many parallelograms are formed when a set of five parallel lines intersect another set of four parallel lines ?

A) 120

B) 60

C) 36

D) 20

E) 10



To form a parallelogram two parallel lines must intersect with two parallel lines

First case we have to select 2 parallel lines from 5 i.e. = 5C2

Second case we have to select 2 parallel lines from 4 i.e. = 4C2

Therefore total no. parallelogram formed = 5C2 * 4C2 = 10 * 6 = 60
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Re: How many parallelograms are formed when a set   [#permalink] 13 Sep 2018, 19:06
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