Subjects combinatorics

Circular Permutation

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Circular Permutation


1. **Problem:** Find the number of possible ways 5 people (Kenshin, Dan, Justin, Kris, Miguel) can be seated in a circular arrangement. 2. **Formula:** For circular permutations, the number of ways to arrange $n$ distinct people around a round table is given by: $$ (n-1)! $$ This is because in a circle, one position is fixed to avoid counting rotations as different arrangements. 3. **Calculation:** Here, $n=5$, so the number of ways is: $$ (5-1)! = 4! = 4 \times 3 \times 2 \times 1 = 24 $$ 4. **Explanation:** Fixing one person’s seat, we arrange the remaining 4 people in any order, resulting in 24 unique circular arrangements. **Final answer:** There are 24 possible ways for Kenshin, Dan, Justin, Kris, and Miguel to be seated around the circular table.