Question

Number of ways in which $10$ different diamonds can be arranged to make a necklace is

• A. $9!$
• B. $\frac{10!}{2}$
• C. $\frac{9!}{2}$
• D. $10!$

Answer 1

The correct option is C $\frac{9!}{2}$

Number of arrangements of $10$ different diamonds around a circle is $(10-1)!$
Since diamonds do not have natural order of left and right so, clockwise and anticlockwise arrangements are taken as identical.
Therefore the number of arrangements of $10$ different diamonds to make a necklace
$=\frac{(10-1)!}{2!}=\frac{9!}{2}$