Question

The number of ways in which 5 beads of different colours form a necklace is

• A. 12
• B. 24
• C. 120
• D. 60

Answer 1

Answer: (A)

12

Answer 2

The number of ways in which 5 beads of different colours can be arranged in a circle to form a necklace are

= $(5 - 1)! = 4!$.

But the clockwise and anticlockwise arrangements are not different (because when the necklace is turned over one gives rise to another). Hence the total number of ways of arranging the beads = $\frac{1}{2}(4!) = 12$.