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Question

Number of circular permutations of n distinct objects is


A

n!

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B

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C

(n-1)!

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D

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Solution

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 = 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)!


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