Here's an example of what I mean by permutations in a closed loop:
A necklace is to be made by threading four identical black beads and four identical white beads onto a string which is closed into a loop. How many different patterns can be made?
What I tried to do to solve this problem was: $4\times 3\times 2\times 1$ (permutations of black beads) multiply with $4\times 3\times 2\times 1$ (permutations of white beads)
However, I discovered that because these beads are in a closed loop (if you visualize this) so...
(W = white beads B = Black beads) WWWBWBBB will be the same as WWWBBBWB or WWWWBBBB = WWWBBBBW
I know I can count all of these by myself (which I did, there are 8 patterns in total), but is there a algebraic way to tackle this sort of problem?