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If m parallel lines in a plane are intersected by a family of n parallel lines, find the number of parallelograms formed?

(a) mn 

(b) (m + 1) (n + 1) 

(c) \(\frac{(m-n)}{n!}\)

(d) \(\frac{mn(n-1)(m-1)}{4}\)

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(d) \(\frac{mn(n-1)(m-1)}{4}\)

A parallelogram is formed by choosing two straight lines from the set of m parallel lines and choosing two straight lines from the set of n parallel lines. 

∴ Number of parallelograms formed = mC2 × nC2

\(\frac{m(m-1)}{2}\times\frac{n(n-1)}{2}\) = \(\frac{mn(n-1)(m-1)}{4}\)

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