6 beads on a necklace (if flipping isn't allowed). (6-1)! = 5! = 120.
If you can flip the necklace (reflection symmetry), divide by 2: 120/2 = 60.
3 people at a round table. (3-1)! = 2! = 2 arrangements.
Circular permutations appear in seating problems and cyclic structures.