Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

In the case of necklace, there is no distribution between the clockwise and anticlockwise arrangements, then the required number of circular permutations

$\frac{⟮\frac{{}^{18}{P}_{12}}{12}⟯}{2}$

= $\frac{18!}{6!\left(24\right)}$

= $\frac{18!}{6!\times 24}$ = $\frac{18\times 17\times 16\times 15\times 14\times 13!}{6\times 5\times 4\times 3\times 2\times 1\times 24}$ = $\frac{119\times 13!}{2}$