How many parallelograms can be formed from a set of 4 parallel lines

To form a parallelogram we need 2 sets of 2 parallel lines intersecting the other 2 lines from the other set. So, first of all, we need to get 2 lines from the sets.

From the first parallel set, 2 out of 4 lines can be selected in ${ }^{4} \mathrm{C}_{2}=6$ ways. From the second parallel set, 2 out of 3 lines can be selected in ${ }^{3} \mathrm{C}_{2}=3$ ways. So, the total number of parallelograms can be formed is $=(6 \times 3)=18$.