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

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Question: How many ways can 6 people be seated around a circular table?

Options:

Correct Answer: 720

Solution:

The number of arrangements around a circular table is (n-1)! = 5! = 120.

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

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

Step 1: Understand that seating people around a circular table is different from a straight line because the arrangement is circular.
Step 2: Realize that in a circular arrangement, one person's position can be fixed to avoid counting the same arrangement multiple times.
Step 3: Since we have 6 people, we can fix one person in one seat.
Step 4: Now, we only need to arrange the remaining 5 people around the table.
Step 5: The number of ways to arrange 5 people in a line is calculated using the factorial of 5, which is written as 5!.
Step 6: Calculate 5! = 5 × 4 × 3 × 2 × 1 = 120.
Step 7: Therefore, the total number of ways to seat 6 people around a circular table is 120.

Circular Permutations – In circular arrangements, one position is fixed to account for rotations, leading to (n-1)! arrangements.