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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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