Number of circular permutations of n distinct objects is
Number of circular arrangements of n distinct objects = (n-1)!
Explanation with an example:
Let us take circular arrangements of letters ABC
As there is neither a begin nor an end position, the following are same arrangements from circular point of view.
ABC BCA CAB
The above figure itself gives 3 arrangements : ACB CBA BAC
So, 3 arrangements can be represented as a single circular arrangement.
So, total circular permutations for 3 objects = 3!3 = 2
Similarly, for N distinct objects , every N permutations can be represented as a circular permutation.
So, the number of circular permutations = Total possible permutations/N = N!N =(N-1)!