find the number of ways of preparing a chain with different coloured beads
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!