Advertisement Remove all ads

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

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads
MCQ

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

Options

  • 6

  •  9

  • 12

  • 18

Advertisement Remove all ads

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
  Is there an error in this question or solution?

APPEARS IN

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

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×