A Parallelogram is Cut by Two Sets of M Lines Parallel to Its Sides. Find the Number of Parallelograms Thus Formed. - Mathematics

A parallelogram is cut by two sets of m lines parallel to its sides. Find the number of parallelograms thus formed.

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 =${}^{m + 2} C_2 \times {}^{m + 2} C_2 = \left( {}^{m + 2} C_2 \right)^2$

Concept: Combination
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Exercise 17.2 | Q 32 | Page 17