There is a set of m parallel lines intersecting a set of another n parallel lines in a plane. The number of parallelograms formed, is m−1C2. n−1C2 mC2. nC2 m−1C2. nC2 mC2. n−1C2

The number of parallelograms formed by m parallel lines intersecting n parallel lines in a plane is given by the formula mC2 * nC2.

Here's the step-by-step solution:

1. mC2 represents the number of ways to choose 2 lines from the m parallel lines. This forms one pair of parallel sides of the parallelogram.

2. Similarly, nC2 represents the number of ways to choose 2 lines from the n parallel lines. This forms the other pair of parallel sides of the parallelogram.

3. Since a parallelogram is defined by two pairs of parallel sides, the total number of parallelograms is the product of the number of ways to choose each pair of sides. Hence, the formula mC2 * nC2.

Note: "mC2" is read as "m choose 2" and represents a combination, which is a way of selecting items from a larger set where order does not matter. It is calculated as m! / [(m-2)! * 2!], where "!" denotes factorial, the product of all positive integers up to that number.