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Question

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

A
14mn(m1)(n1)
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B
12mn(m1)(n1)
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C
14m2n2
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D
None of these
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Solution

The correct option is B 14mn(m1)(n1)
The number of selection of two parallel lines from m lines is mC2.
The number of selection of two parallel lines from n lines is nC2.
Hence, the number of parallelograms lines is
mC2×nC2=14mn(m1)(n1)

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