Circular Permutations

If we arrange objects along a closed curve for example a circle, the permutations are known as circular permutations. In a circular permutation, we have to consider one object as fixed and the remaining are arranged as in case of linear arrangement.

Linear arrangement is arrangement in a row.

Theorem
The number of circular permutations of n distinct objects is (n-1)!.

Anti-clock wise and clockwise order of arrangements are considered as distinct permutations in the above theorem.

If the anticlockwise and clockwise order is not distinct as in case of a garland which can be turned over easily, the number of distinct permutations will be ½ (n-1)!