Question

A parallelogram is cut by two sets of m lines parallel to its sides as shown. The number of parallelograms thus formed is_______.

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is C

Each set is having in m+2 parallel lines and each parallelogram is formed by choosing two

straight lines from the first set and two straight lines from the second set. Two straight

lines from the first set can be chosen in ${}^{m+2}{C}_2$ ways and two straight lines from the second

set can be chosen in ${}^{m+2}{C}_2$ ways.

Hence the total number of parallelograms formed =${}^{m+2}{C}_2$ . ${}^{m+2}{C}_2$ = ( ${}^{m+2}{C}_2{)}^2$.
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