The number of parallelograms that can be form | vedclass

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(B) To form a parallelogram,we need to select $2$ lines from the first set of $4$ parallel lines and $2$ lines from the second set of $3$ parallel lin

Vedclass · Accepted Answer

$18$

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(B) To form a parallelogram,we need to select $2$ lines from the first set of $4$ parallel lines and $2$ lines from the second set of $3$ parallel lines.The number of ways to select $2$ lines from $4$ is given by $^{4}C_{2} = \frac{4 	imes 3}{2 	imes 1} = 6$.The number of ways to select $2$ lines from $3$ is given by $^{3}C_{2} = \frac{3 	imes 2}{2 	imes 1} = 3$.The total number of parallelograms is the product of these two combinations:Total $= ^{4}C_{2} 	imes ^{3}C_{2} = 6 	imes 3 = 18$.

The number of parallelograms that can be formed from a set of $4$ parallel lines intersecting another set of $3$ parallel lines is:

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