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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:
- 45
- 24
- 12
- 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
- 2520
- 5040
- 360
- 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
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