How many different ways can 4 people be seated at a round table?

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Question: How many different ways can 4 people be seated at a round table?

Options:

Correct Answer: 12

Solution:

The number of arrangements of n people at a round table is (n-1)!. For 4 people, it is 3! = 6.

How many different ways can 4 people be seated at a round table?

How many different ways can 4 people be seated at a round table?

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

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