# The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is

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

Solution:

(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.

$\therefore$ Number of parallelograms that can be formed $={ }^{4} C_{2} \times{ }^{3} C_{2}=\frac{4 !}{2 ! 2 !} \times \frac{3 !}{2 ! 1 !}=6 \times 3=18$