# Formulas For Circular Permutations

## Formulas of Circular Permutations in Aptitude

When we calculate the number of way of arranging the items in closed loop or in a circular manner , known as Circular Permutation. In this Page Formulas of Circular Permutations is given. ### Formula

Number of circular-permutations of ‘n’ different things taken ‘r’ at a time:-

Case 1: If clock-wise and anti-clockwise orders are taken as different, then total number of circular-permutations = $\frac{^nP_r}{r}$

Case 2: If clock-wise and anti-clockwise orders are taken as not different, then total number of circular – permutation = $\frac{^nP_r}{2r}$

### Formulas & Definition for Circular Permutations:

• The arrangements we have considered so far are linear. There are also arrangements in closed loops, called circular arrangements. There are two cases of circular-permutations:
• 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 $\frac{(n-1)!}{2!}$
• The number of ways to arrange distinct objects along a fixed (i.e., cannot be picked up out of the plane and turned over) circle is (n-1)!

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