Question

The number of ways that 8 beads of different colours can be strung to form a necklace is

• A. \(5040\)
• B. \(2520\)
• C. \(2840\)
• D. \(5080\)

Hint:

For a necklace of n distinct beads the count is (n-1)!/2.

Answer 1

The Correct Option is B

Step 1: Fix one bead:
Fix one bead to remove rotations. The other 7 beads can be placed in $7!=5040$ ways around it.

Step 2: Remove mirror images:
A necklace can be turned over, so each pattern and its mirror image are the same. Divide by 2: $5040/2=2520$.

Step 3: Pick:
Option B.

Final Answer:
Seven factorial divided by two gives 2520. \[ \boxed{\text{(B) }2520} \]