Circular Permutations

Question

In how many ways can 5 beads of different colors be arranged to form a necklace?

RankGuru · Accepted Answer

1. **Symmetry Analysis**: In a necklace, we can flip it over. This means clockwise and anti-clockwise arrangements are considered identical (reflectional symmetry).
2. **Formula**: $\frac{(n-1)!}{2}$.
3. **Substitution**: For $n=5$.
4. **Calculation**:
   - $\frac{(5-1)!}{2} = \frac{4!}{2} = \frac{24}{2} = 12$.
5. **Note**: If the beads were on a table where they couldn't be flipped, the answer would be 24.

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Circular Permutations

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