Tips And Tricks And Shortcuts for Circular Permutation Questions

December 14, 2020

Tips and Tricks nd Shortcuts for Permutations Questions Quickly

The Calculation of the number of ways to arranging the objects, items or peoples in closed loop or in a circular manner referred as Circular Permutation.

Tips and Tricks & Shortcuts to Solve Circular Permutations

- Circular Permutation are arrangements in the closed loops.
- If clockwise and anti-clock-wise orders are different, then total number of circular-permutations is given by (n-1)!
- If clock-wise and anti-clock-wise orders are taken as not different, then total number of circular-permutations is given by $\frac{(n-1)!}{2!}$
- Here, are quick and easy tips and tricks for you to solve Circular Permutation questions quickly, easily, and efficiently in competitive exams.

Type 1: When clockwise and anticlockwise arrangements are different.

Trick: Number of circular permutations (arrangements) of n distinct things when arrangments are different = (n−1)!

Question 1. In how many ways can 5 girls be seated in a circular order?

Options:

1. 1. 45
  2. 24
  3. 12
  4. 120

Solution Number of arrangements possible = (5 − 1)!

= 4!

= 4 * 3 * 2 * 1

= 24

Correct option: 2

Type 2: When clockwise and anticlockwise arrangements are not different

Tips & Trick: Number of circular permutations (arrangements) of n distinct things when arrangements are not different = $\frac{1}{2}$ × (n−1)!

Question 1. In how many ways can 8 beads can be arranged to form a necklace?

Options

1. 1. 2520
  2. 5040
  3. 360
  4. 1200

Solution Number of arrangements possible = $\frac{1}{2}$ × (n−1)!

$\frac{1}{2}$ × (8−1)!

$\frac{1}{2}$ × 7!

$\frac{1}{2}$ × 5040 = 2520

Correct option: 1