The number of ways in which 5 beads of different colours can be made into a necklace is

Options

A. 12
B. 120
C. 60
D. 24

Answer

To find the number of ways in which 5 beads of different colors can be made into a necklace, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Circular Permutation**:
When arranging items in a circle, we need to consider that rotations of the same arrangement are not distinct. Therefore, the formula for arranging \( n \) items in a circle is given by \( (n-1)! \).

2. **Identify the Number of Beads**:
In this case, we have 5 beads of different colors. So, \( n = 5 \).

3. **Apply the Formula**:
Using the circular permutation formula:
\[ \text{Number of arrangements} = (n-1)! = (5-1)! = 4! \]

4. **Calculate Factorial**:
Now, we need to calculate \( 4! \):
\[ 4! = 4 \times 3 \times 2 \times 1 = 24 \]

5. **Conclusion**:
Therefore, the number of ways to arrange 5 beads of different colors into a necklace is \( 24 \).

### Final Answer:
The number of ways in which 5 beads of different colors can be made into a necklace is **24**.