Question

In how many ways can 6 people be seated around a circular table? 
 

• A. 120
• B. 360
• C. 720
• D. 1440

Hint:

For circular seating, fix one position to remove identical rotations, then arrange the rest.

Answer 1

The Correct Option is A

Step 1: Understanding Circular Permutations

In a linear arrangement, n people can be seated in n! ways.
However, in a circular arrangement, the arrangements that are rotations of each other are considered the same.
This means we fix one person’s seat to break the rotational symmetry and arrange the remaining (n − 1) people.

Step 2: Formula for Circular Permutations

The formula for the number of ways to arrange n distinct people around a circle is:

Number of arrangements = (n - 1)!
    

Step 3: Applying the Formula

Here, n = 6 people.
Using the formula:

Number of arrangements = (6 - 1)! 
                        = 5!
                        = 120
    

Step 4: Final Answer

The number of ways 6 people can be seated around a circular table is:
120 ways.