Question

There is a set of $m$ parallel lines intersecting a set of another $n$ parallel lines in a plane. The number of parallelograms formed, is

• A. ${}^{m-1}{C}_2\times {}^{n-1}C_2$
• B. ${}^m{C}_2\times {}^{n}C_2$
• C. ${}^{m-1}{C}_2\times {}^{n}C_2$
• D. ${}^m{C}_2\times {}^{n-1}C_2$

Answer 1

The correct option is B

${}^m{C}_2\times {}^{n}C_2$

Explanation for the correct answer:

Compute the required number:

A parallelogram is created when two sets of two parallel lines intersect each other.

To form a parallelogram out of the given lines,

We must select $2$ lines from the first set of $m$ lines and 2 lines from the second set of $n$ lines.

Ways of selecting $2$ lines from $m$$={}^m{C}_2$

Ways of selecting $2$ lines from $n$$={}^n{C}_2$

The total number of parallelograms formed$={}^m{C}_2\times {}^{n}C_2$

Hence, option $\left(B\right)$is the correct answer.