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

Solution:

We know if m parallel lines are intersected by family of n parallel lines then number of parallelograms

${=}^{\mathrm{m}}{\mathrm{C}}_2{\times }^{\mathrm{n}}{\mathrm{C}}_2=\frac{\mathrm{mn}(\mathrm{m}-1)(\mathrm{n}-1)}{4}$

In given ques, $m = 4, n = 3$ 

$\therefore$Number of parallelogram formed $=\frac{12\left(3\right)\left(2\right)}{4}=18.$