Question

Number of circular permutations of n distinct objects is

• A. n!
• B.
• C. (n-1)!
• D.

Answer 1

The correct option is C

(n-1)!

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 = $\frac{3!}{3}$ = 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 = $\frac{N!}{N}$ =(N-1)!