Question

The number of ways in which 5 different beads can be arranged to form a necklace is :

• A. 24
• B. 120
• C. 12
• D. 18

Answer 1

Answer:

C. 12

The number of ways in which 5 different beads can be arranged to form a necklace is 12

When arranging objects in a necklace, we use the formula for circular permutations where clockwise and counter-clockwise arrangements are considered identical (since a necklace can be flipped over):

$\text{Number of ways} = \frac{(n - 1)!}{2}$

Where $n$ is the number of different beads.

Plugging in $n = 5$:
$\text{Number of ways} = \frac{(5 - 1)!}{2} = \frac{4!}{2}$
$\text{Number of ways} = \frac{24}{2} = 12$