4 votes 4 votes A set of $4$ parallel lines intersect with another set of $5$ parallel lines. How many parallelograms are formed? $20$ $48$ $60$ $72$ Quantitative Aptitude gate2018-ch general-aptitude quantitative-aptitude easy geometry + – Lakshman Bhaiya asked Feb 20, 2018 edited Jun 2, 2019 by Lakshman Bhaiya Lakshman Bhaiya 2.9k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 11 votes 11 votes 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 Rishabh Gupta 2 answered Feb 20, 2018 edited Jun 20, 2019 by ajaysoni1924 Rishabh Gupta 2 comment Share Follow See all 0 reply Please log in or register to add a comment.