Question

How many necklace $12$ beads each can be made out of $18$ beads of different colors

• A. ${}^{18}{P}_{12}$
• B. $\frac{18!}{6!\times 24}$
• C. ${}^{18}{C}_{12}\times \frac{11!}{2!}$
• D. None of these

Answer 1

The correct option is C ${}^{18}{C}_{12}\times \frac{11!}{2!}$

Select $12$ beads from $18$ beads and then arrange them according to circular permutations.

${}^{18}{C}_{12}\times \frac{(12-1)!}{2!}$

${}^{18}{C}_{12}\times \frac{\left(11\right)!}{2!}$