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Q.
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines:
Permutations and Combinations
Solution:
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 $