If m parallel lines in a plane are intersected by a family of n parallel lines, the number of parallelograms that can be formed is

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14mn(m−1)(n−1)

12mn(m−1)(n−1)

14m2n2

none of these

answer is A.

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Detailed Solution

The number of selection of two parallel lines from la lines is mC2.The number of selection of two parallel lines from n lines is nC2.Hence, the number of parallelograms is mC2×nC2=14mn(m−1)(n−1)

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