Formulas For Circular Permutations

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)!