Question

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

• A. 6
• B. 9
• C. 18
• D. 12

Answer 1

Answer: (C)

18

Answer 2

We know if m parallel lines are intersected by family of n parallel lines then number of parallelograms $= {^mC_2} \times {^nC_2} = \frac{mn(m-1)(n-1)}{4}$ In given ques, m = 4, n = 3 $\therefore$ Number of parallelogram formed $= \frac{12(3)(2)}{4} = 18$