Circular arrangement:
- Number of ways of arranging $$n$$ items around a circle are $$1$$ for $$n=1,2$$ and $$(n-1)!$$ For $$n\ge 3$$
- Circular arrangement of beads/necklace (no fixed direction) = (n-1)!/2
- In general, when the positions (placeholder seats) are identical in a circular arrangement problem, the arrangement are calculated for $$(n-1)$$ objects, after fixing $$1$$ object.