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

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

1. A

6

2. B

9

3. C

18

4. D

12

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### Solution:

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

${=}^{\mathrm{m}}{\mathrm{C}}_{2}{×}^{\mathrm{n}}{\mathrm{C}}_{2}=\frac{\mathrm{mn}\left(\mathrm{m}-1\right)\left(\mathrm{n}-1\right)}{4}$

In given ques,

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

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