How many ways can 6 people be seated at a round table? (2020)

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Question: How many ways can 6 people be seated at a round table? (2020)

Options:

Correct Answer: 720

Exam Year: 2020

Solution:

The number of arrangements of 6 people at a round table is (6-1)! = 5! = 120.

How many ways can 6 people be seated at a round table? (2020)

How many ways can 6 people be seated at a round table? (2020)

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: Since we have 6 people, we can fix one person in one seat. This leaves us with 5 people to arrange.
Step 4: Calculate the number of ways to arrange the remaining 5 people. This is done by finding the factorial of 5, which is written as 5!.
Step 5: Calculate 5! = 5 × 4 × 3 × 2 × 1 = 120.
Step 6: Conclude that the total number of ways to seat 6 people at a round table is 120.

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