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Question
A parallelogram is cut by two sets of m lines parallel to its sides. Find the number of parallelograms thus formed.
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Solution
Each set of parallel lines consists of \[\left( m + 2 \right)\] lines.
Each parallelogram is formed by choosing two lines from the first set and two straight lines from the second set.
∴ Total number of parallelograms =\[{}^{m + 2} C_2 \times {}^{m + 2} C_2 = \left( {}^{m + 2} C_2 \right)^2\]
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