In how many ways can 6 beads of same colour form a neclace ?

Answer

To find the number of ways to arrange 6 beads of the same color into a necklace, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**: We have 6 beads, all of the same color. When forming a necklace, we need to consider that arrangements that can be rotated or flipped are considered the same.

2. **Using the Formula for Necklaces**: The formula for the number of distinct arrangements of n identical beads in a necklace is given by:
\[ \text{Number of necklaces} = \frac{n!}{2n} \]
where \( n \) is the number of beads.

3. **Substituting the Values**: In this case, \( n = 6 \).
\[ \text{Number of necklaces} = \frac{6!}{2 \times 6} \]

4. **Calculating Factorial**: First, we calculate \( 6! \):
\[ 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720 \]

5. **Calculating the Number of Necklaces**:
\[ \text{Number of necklaces} = \frac{720}{12} = 60 \]

6. **Final Result**: Therefore, the number of distinct ways to arrange 6 beads of the same color into a necklace is:
\[ \text{Number of distinct necklaces} = 1 \]

### Conclusion:
Since all the beads are of the same color, any arrangement will look identical. Thus, there is only **1 way** to form a necklace with 6 beads of the same color.