Question

A parallelogram is cut by two set of $m$ lines parallel to its sides. The number of parallelogram thus force is

• A. ${(}^m{C}_2{)}^2$
• B. ${(}^{m+1}{C}_2{)}^2$
• C. ${(}^{m+2}{C}_2{)}^2$
• D. ${}^{m+1}{C}_2$

Answer 1

The correct option is C ${(}^{m+2}{C}_2{)}^2$

parallelogram is cut by two sets of m parallel lines to its sides.
then we have  2 sets of (m+2) parallel lines ( 2 lines of the parallelogram)
so parallelogram is formed by taking 2 lines from each set
 = m+2C2 * m+2C2