Circular permutation is the total number of ways in which n distinct objects can be arranged around a fix circle. It is of two types.

1. **Case 1: **– Clockwise and Anticlockwise orders are different.

2. **Case 2: **– Clockwise and Anticlockwise orders are same.

__Case 1: Formula__

__Case 1: Formula__

Pn=(n−1)!Pn=(n−1)!

Where −

· PnPn = represents circular permutation

· nn = Number of objects

__Case 2: Formula__

__Case 2: Formula__

Pn=n−1!2!Pn=n−1!2!

Where −

· PnPn = represents circular permutation

· nn = Number of objects

__Example__

__Example__

**Problem Statement:**

Calculate circular permulation of 4 persons sitting around a round table considering i) Clockwise and Anticlockwise orders as different and ii) Clockwise and Anticlockwise orders as same.

**Solution:**

In Case 1, n = 4, Using formula

Pn=(n−1)!Pn=(n−1)!

Apply the formula

P4=(4−1)! =3! =6P4=(4−1)! =3! =6

In Case 2, n = 4, Using formula

Pn=n−1!2!Pn=n−1!2!

Apply the formula

P4=n−1!2! =4−1!2! =3!2! =62 =3