Question

In how many ways can a necklace with 8 beads of different colors be made?
1. 5,040
2. 2,880
3. 2,520
4. 1,440

Answer 1

Correct Answer - Option 3 : 2,520

Given: 

The number of beads are 8

Concept Used: 

No. of ways = (n - 1)!

Calculation: 

A necklace is circular,

Let fix Position of one Bead

Then 7 beads can be arranged into 7! 

⇒ Ways = 7 × 6 × 5 × 4 × × 3 × 2 × 1 = 5,040

Now as it a necklace and if it can be wear from both sides

Flipping its sides will reduce ways to half

Hence Number of Ways,

⇒ 5,040/2 = 2,520

∴ The number of ways is 2,520