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Circular permutation

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Circular permutation

Posted by Khush Agarwal 3 years, 11 months ago

CBSE > Class 11 > Applied Maths

1 answers

Gaurav Seth 3 years, 11 months ago

So the important point about circular arrangement is as follows:

If the clockwise and counter clockwise orders CAN be distinguished then total number of circular permutation of n elements taken all together = (n-1)!
If the clockwise and counter clockwise orders CANNOT be distinguished then total number of circular permutation of n elements taken all together = (n-1)! / 2

Example of indistinguishable case is, if you consider 5 diamonds and you want to make a necklace. In this case 5 diamonds can be arranged in a circle in (5-1)! = 24 ways. But in case of forming a necklace the clockwise and counter clockwise arrangements cannot be distinguished. So the total circular permutation in this case = (5-1)! / 2 = 4! / 2 = 12 ways.

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