GATE2018 CH: GA-7

Question

A set of $4$ parallel lines intersect with another set of $5$ parallel lines. How many parallelograms are formed?

• A. $20$
• B. $48$
• C. $60$
• D. $72$

Answer 1

If we choose any 2 of the 4 lines and any 2 of the 5 lines we will get a parallelogram. This way we can count all the possibilities.

$\binom{4}{2} * \binom{5}{2} = 6 * 10 = 60$

Here, the first term is the ways of choosing 2 lines out of 4 parallel lines, and the second term is for choosing 2 lines out of 5 parallel lines.

Option (C) 60

https://math.stackexchange.com/questions/772062/parallelograms-formed-by-parallel-lines

http://clay6.com/qa/40004/the-number-of-parallelogram-that-can-be-formed-from-a-set-of-four-parallel-

https://www.quora.com/How-many-parallelograms-are-formed-by-a-set-of-4-parallel-lines-intersecting-another-set-of-7-parallel-lines