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Suppose, 20 parallel railway tracks are intersected by another 30 parallel railway tracks. How many parallelograms will be formed by the intersection of these railway tracks?

Suppose, 20 parallel railway tracks are intersected by another 30 parallel railway tracks. How many parallelograms will be formed by the intersection of these railway tracks? Correct Answer 82, 650

A parallelogram is formed when two parallel lines are intersected by other two parallel lines.

Two parallel lines can be chosen from a set of 20 parallel lines in 20C2 ways.

Two parallel lines can be chosen from a set of 30 parallel lines in 30C2 ways.

Hence, the total number of parallelograms formed = 20C2 × 30C2 = 20(20 - 1)/2 × (30(30 - 1))/2 = (20(19)(30)(29))/4 = 82, 650

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