Question

The number of ways in which $8$ beads of different colours be strung in a necklace is

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

Answer 1

Answer: (A)

$2520$

Here $7$ beads of different colors taken all at a time can be arranged in $(8-1)!=7!$ ways along a circle.

Further in the case of formation of necklace, the clockwise and anti - clockwise arrangements are same.

Hence, the required numbers formed $=\frac{1}{2}\times 7!=\frac{1}{2}\left(5040\right)=2520$