The number of parallelograms that can be form | vedclass

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(B) To form a parallelogram,we need to select two lines from the first set of four parallel lines and two lines from the second set of three parallel

Vedclass · Accepted Answer

$18$

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(B) To form a parallelogram,we need to select two lines from the first set of four parallel lines and two lines from the second set of three parallel lines.The number of ways to select $2$ lines from $4$ is given by the combination formula $^nC_r = \frac{n!}{r!(n-r)!}$.Number of ways to choose $2$ lines from $4 = ^4C_2 = \frac{4 	imes 3}{2 	imes 1} = 6$.Number of ways to choose $2$ lines from $3 = ^3C_2 = \frac{3 	imes 2}{2 	imes 1} = 3$.Since these selections are independent,the total number of parallelograms is the product of these two values:Total parallelograms $= 6 	imes 3 = 18$.

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

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