Question

In how many ways can $10$ different beads be arranged to from a necklace so that $4$ beads are always a like?

Answer 1

Number of ways to arrange 10 beads to form a necklace $=\frac{(10-1)!}{2}=\frac{9!}{2}$

But , $4$ beads are a like

Total arrangements $=\frac{9!}{2\times 4!}$