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📐 Mathematics  ·  Permutations and Combinations  ·  JEE

Number of ways to arrange n people in a circle with one fixed (labeled) position:

Answer: (n-1)!.

  • A n!
  • B (n-1)!
  • C n!/2
  • D

Correct answer: B. (n-1)!

Explanation: Circular permutation: fix one person to remove rotational equivalence. The remaining n−1 people arrange linearly in (n−1)! ways. Answer: (n−1)!.

StartABCBCACAB6 ordered outcomes (permutations); pairing AB/BA etc gives 3 combinations

Counting tree for selecting 2 items from {A, B, C} without repetition: 3 x 2 = 6 ordered arrangements.

Concept context

Counting, arrangements, and selections

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