Circular Permutation
The permutation of n objects arranged in a circle is P = (n - 1)!
Example: How many ways can 4 people be seated around a circular table? Solution: n = 4 (Let us call the 4 people A, B, C, D)
Exercises: Find the number of permutations of the following people arranged in a circle
Example: 4 people Solution: P = (n - 1)! = (4 - 1)! = 3! = 3 * 2 * 1 = 6
1. 5 people
2. 6 people
3. 8 people
4. 10 people
The number of permutations of n objects taken r at a time denoted by P(n, r), where n ≥ r is P(n, r) = n(n - 1)(n - 2) ... (n - r + 1). In addition, since P(n, r) = n(n - 1)(n - 2) ... (n - r + 1), P(n, r) = [n(n - 1)(n - 2) ... (n - r + 1)(n - r)!] / (n - r)!