Understanding Circular Permutations Formulae

In this class, We discuss Understanding Circular Permutations Formulae.

The reader should have prior knowledge of permutation basics. Click Here.

First, refresh the concept of linear arrangements.

Take an example characters A, B, C, D, E.

By shifting the characters one step right, we make one more arrangement E, A, B, C, D.

Again, shift one position right, we make another arrangement D, E, A, B, C.

The shifting of characters will not work in circular permutations.

Take a pattern A, B, C, D, E.

By shifting, the positions still get the same pattern circularly.

The diagram below shows the difference in the shift.

For each pattern, we miss N arrangements.

The formulae for circular arrangements are given N!/N

The formula for circular arrangements is (N-1)!