Circular Permutations
In how many ways can 5 beads of different colors be arranged to form a necklace?
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About This Question
- Subject
- mathematics
- Chapter
- permutations and combinations
- Topic
- circular permutations
- Difficulty
- Hard
- Year
- 2025
Solution
Correct Answer:
12
- Symmetry Analysis: In a necklace, we can flip it over. This means clockwise and anti-clockwise arrangements are considered identical (reflectional symmetry).
- Formula: 2(n−1)!.
- Substitution: For n=5.
- Calculation:
- 2(5−1)!=24!=224=12.
- Note: If the beads were on a table where they couldn't be flipped, the answer would be 24.
This hard difficulty mathematics question is from the chapter permutations and combinations, covering the topic of circular permutations. It appeared in the 2025 exam.
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