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(B) parallelogram is formed by selecting two parallel lines from the first set of $4$ parallel lines and two parallel lines from the second set of $3$

Vedclass · Accepted Answer

$18$

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(B) parallelogram is formed by selecting two parallel lines from the first set of $4$ parallel lines and two parallel lines from the second set of $3$ parallel lines.$	herefore$ Total number of parallelograms formed = (Number of ways to select $2$ lines from the first set) $	imes$ (Number of ways to select $2$ lines from the second set).$	herefore$ Total number of parallelograms = ${}^4C_2 	imes {}^3C_2$.Using the formula ${}^nC_r = \frac{n!}{r!(n-r)!}$:${}^4C_2 = \frac{4 	imes 3}{2 	imes 1} = 6$.${}^3C_2 = \frac{3 	imes 2}{2 	imes 1} = 3$.$	herefore$ Total number of parallelograms = $6 	imes 3 = 18$.

How many parallelograms can be formed by a set of $4$ parallel lines intersecting another set of $3$ parallel lines?

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