# Tips And Tricks And Shortcuts for Circular Permutation Questions

## 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. 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. 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

Read Also – How to solve circular permutation questions