Question

How many necklaces of 12 beads can be made from 18 beads of various colours?

• A. $\frac{119\times 13!}{2}$
• B. $\frac{110\times 14!}{2}$
• C. $\frac{153\times 11!}{2}$
• D. $\frac{110\times 12!}{2}$

Answer 1

The correct option is C $\frac{153\times 11!}{2}$

Selecting 12 beads out of 18 = ${}^{18}{C}_{12}$
Making a necklace = $\frac{11!}{2}$
Total =${}^{18}{C}_2\times \frac{11!}{2}=\frac{153\times 11!}{2}$