Question

Type the formula for the number of circular permutations of n things. Pc(n,n) = ?

I don't know how to do this, can someone please explain? Thanks!

Answer 1

If the clockwise and anti-clockwise orders are different the total number of circular permutations is (n - 1)!
If the clockwise and anti-clockwise orders are the same the total number of circular permutations is
\[\frac{(n-1)!}{2!}\]

Answer 2

okay! thanks!

Answer 3

You're welcome :)

Answer 4

First of all, let's understand what it means.
To understand a circular permutation, imagine a circle with spots on it to place numbers in, like this

And we want to write in our numbers, 1 through 5. How many different ways can we write all of our numbers?

Answer 5

Or there could be a different number of spots. But that's the question. That's a circular permutation.

Answer 6

Now, the interesting thing about this question is this. Do I count these two things as totally different possibilities?