Question

Find the number of parallelogram formed if 10 parallel lines in a plane are intersected by a family of 12 parallel lines.

Answer 1

A parallelogram is formed by choosing two straight lines 2 lines from the set of 10 lines and 2 lines from the set of 12 parallel lines.

Two parallel lines can be chosen from the set of 10 parallel lines in ${}^{10}{C}_2$ ways.

Two parallel lines can be chosen from the set of 12 parallel lines in ${}^{12}{C}_2$ ways.

Hence, the number of parallelogram formed ${=}^{10}{C}_2{\times }^{12}{C}_2$

$=\frac{10!}{2!8!}\times \frac{12!}{2!10!}$

$=\frac{10\times 9}{2}\times \frac{12\times 11}{2}$

$=2970$