What is the formula to find the no of the possible circular permutation?
Answers
Answer:The number of ways to arrange n distinct objects along a fixed (i.e., cannot be picked up out of the plane and turned over) circle is
P_n=(n-1)!.
Step-by-step explanation:
The number is (n-1)! instead of the usual factorial n! since all cyclic permutations of objects are equivalent because the circle can be rotated.
For example, of the 3!=6 permutations of three objects, the (3-1)!=2 distinct circular permutations are {1,2,3} and {1,3,2}. Similarly, of the 4!=24 permutations of four objects, the (4-1)!=6 distinct circular permutations are {1,2,3,4}, {1,2,4,3}, {1,3,2,4}, {1,3,4,2}, {1,4,2,3}, and {1,4,3,2}. Of these, there are only three free permutations (i.e., in equivalent when flipping the circle is allowed): {1,2,3,4}, {1,2,4,3}, and {1,3,2,4}. The number of free circular permutations of order n is P_n^'=1 for n=1, 2, and
P_n^'=1/2(n-1)!
for n>=3, giving the sequence 1, 1, 1, 3, 12, 60,