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

$\frac{1}{2} mn (m - 1) (n - 1)$

$\frac{1}{4} m^{2} n^{2}$

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answer is A.

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Detailed Solution

The number of selection of two parallel lines from la lines is $^{m} C_{2}$ .

The number of selection of two parallel lines from n lines is $^{n} C_{2}$ .

Hence, the number of parallelograms is

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

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