This is a problem of circular permutations. For such problems there is a well known formulae using which we use to solve it.

No of circular permutations possible for n-distinct beads is given by: 1/2(n-1)!

This is the formulae where you can plug the number of beads in order to get the number of Circular Permutations.

I hope my answer helps. All the very best for your future endeavors!