Question

The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is
(a) 6
(b) 9
(c) 12
(d) 18

Answer 1

(d) 18
A parallelogram can be formed by choosing two parallel lines from the set of four parallel lines and two parallel lines from the set of three parallel lines.
Two parallel lines from the set of four parallel lines can be chosen in ⁴C₂ ways and two parallel lines from the set of 3 parallel lines can be chosen in ³C₂ ways.
∴ Number of parallelograms that can be formed = ${}^{4}C_2\times {}^{3}C_2=\frac{4!}{2!2!}\times \frac{3!}{2!1!}=6\times 3=18$