A parallelogram is cut by two set of n parallel lines, parallel to the sides of the parallelogram. The number of parallelograms formed is

A parallelogram is intersected by 2 sets of n parallel lines.

$\therefore$ There are  2 sets of (m+2) parallel lines

Number of parallelograms formed

$\begin{array}{rcl} & =& {(\mathrm{n}+2)}_{{\mathrm{C}}_2}\times {(\mathrm{n}+2)}_{{\mathrm{C}}_2}\\ & =& {\left(\mathrm{n}+2_{{\mathrm{C}}_2}\right)}^2 \end{array}$