Subjects combinatorics

Circular Permutation

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Circular Permutation


1. **Problem:** Find the number of possible seating arrangements for Kenshin, Dan, Justin, Kris, and Miguel around a circular table. 2. **Formula:** For $n$ people seated around a circular table, the number of distinct arrangements is given by: $$ (n-1)! $$ This is because in circular permutations, one position is fixed to avoid counting rotations as different arrangements. 3. **Calculation:** Here, $n=5$. $$ (5-1)! = 4! = 4 \times 3 \times 2 \times 1 = 24 $$ 4. **Answer:** There are 24 possible ways for Kenshin, Dan, Justin, Kris, and Miguel to be seated around the circular table. --- Since the user asked multiple questions but per instructions we solve only the first one completely, we stop here.