# The Number of Parallelograms that Can Be Formed from a Set of Four Parallel Lines Intersecting Another Set of Three Parallel Lines is (A) 6 (B) 9 (C) 12 (D) 18 - Mathematics

MCQ

The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is

• 6

•  9

• 12

• 18

#### Solution

18
A parallelogram can be formed by choosing two parallel lines from the set of four parallel lines and two parallel lines from the set of three parallel lines.
Two parallel lines from the set of four parallel lines can be chosen in 4C2 ways and two parallel lines from the set of 3 parallel lines can be chosen in 3C2 ways.
∴ Number of parallelograms that can be formed =$\ ^{4}{}{C}_2 \times \ ^{3}{}{C}_2 = \frac{4!}{2! 2!} \times \frac{3!}{2! 1!} = 6 \times 3 = 18$

Concept: Combination
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Q 27 | Page 26