Question

There are two sets of parallel lines-one contains m lines and the other n lines. How many parallelograms are formed by these two sets?

• A. ${}^m{C}_2$ . ${}^n{C}_2$
• B. ${}^m{C}_1$ . ${}^n{C}_2$
• C. ${}^m{C}_2$ . ${}^n{C}_3$
• D. None of these

Answer 1

The correct option is A ${}^m{C}_2$ . ${}^n{C}_2$

We have two sets of parallel lines. Assuming that the two sets are not parallel to each other, we can say that some parallelograms will be formed. We need to determine the number of parallelograms.

We have to select any two lines from each set.

From one set we can do it in ${}^m{C}_2$ ways.

From the other we can do it in ${}^n{C}_2$ ways.

As the work is not completed only by selecting, we have to multiply the above results.

$={}^n{C}_2$*${}^m{C}_2$

So ${}^n{C}_2$*${}^m{C}_2$ parallelograms will be formed