Question

Find the number of ways in which 410 different diamonds can be arranged to make a necklace.

Answer 1

$410$ diamond have to be arranged in a circular shape

no of ways $=\frac{(410-1)!}{2}\Rightarrow \frac{\left(409\right)!}{2}$

$\therefore 410$ different diamonds can be arranged to make a round necklace in $\frac{\left(409\right)!}{2}$ ways