We know that parallelogram has 4 lines in which 2 sides are parallel to each other which means 2 pairs of lines are parallel lines

It is told that parallelogram is cut by two sets of m lines parallel to its sides.

This means there will be two sets of (m + 2) lines parallel to each other.

We need two sets of parallel lines to form a parallelogram in which the lines need to be chosen from these two sets of (m + 2) parallel lines.

Let us assume that the no. of parallelograms formed be N.

⇒ N = (choosing 2 parallel lines from (m + 2) parallel lines which are parallel to one side) × (choosing 2 parallel lines from (m + 2) parallel lines which are parallel to the side which is not parallel to the first side)

⇒ N = (^{m + 2}C₂) × (^{m + 2}C₂)

⇒ N = (^{m + 2}C₂)²

We know that ,

And also n! = (n)(n – 1)......2.1

⇒

⇒

⇒

⇒

∴ The total no. of parallelograms formed are .