Question

How many necklaces of $10$ beads each can be made from $20$ beads of different colors?

• A. $19!$
• B. $\frac{19!}{10!}$
• C. $\frac{19!}{10{!}^2}$
• D. $20!$

Answer 1

The correct option is C $\frac{19!}{10{!}^2}$

$10$ Beads $⟶$ Each necklece

$20$ Beads total

Number of ways of arranging $20$ Beads in circular Form $=19!$

There should be $2$ sets of necklace of $10$ beads each

Number of ways $=10!\times 10!$

Total ways

$=\frac{19!}{10!\times 10!}=\frac{19!}{{(10!)}^2}$