Question

The number of ways that $8$ beads of different colors be string as a necklace is?

• A. $2520$
• B. $2880$
• C. $5040$
• D. $4320$

Answer 1

The correct option is A

$2520$

Find the number of combination ways for the given condition

The beads of a necklace follow circular arrangement

$n$ objects can be arranged in $\left(n-1\right)!$ ways around a circle.

Hence the $8$ beads are arranged in $7!$ ways.

Further, both the clockwise and anticlockwise arrangements of a necklace are the same.

Hence, the required number of arrangements $=\frac{7!}{2}=\frac{5040}{2}=2520$

so, the $8$ beads can be arranged in $2520$ ways to form a necklace,

Hence the correct option is $\left(A\right)$