circular r-permutations of n

combinatorics permutations

My book, Discrete Mathematics And Its Applications by K.H.Rosen asks to find a formula for circular r-permutations of n people. That is, sitting of r of these people around a table when two sittings are considered equal if they look the same by rotation of the table.

As I searched, the answer must be, P(n,r)/2r but the book says something different:

The books answer.

So my problem is why? Why do we divide by r and not by 2 at the end? And why didn't "design the head" step divide the answer by r?


Solution 1:

What you probably got the answer is the "bracelet problem", what is being asked is the "necklace problem". The difference is the bracelet is assumed to be equivalent under reflection, whereas necklace is not. see wikipedia article here

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