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

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

Options:

  1. 720
  2. 120
  3. 60
  4. 30

Correct Answer: 120

Solution: 

The number of ways to arrange 6 people around a circular table is (6-1)! = 5! = 120.

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

Practice Questions

Q1
In how many ways can 6 people be seated around a circular table?
  1. 720
  2. 120
  3. 60
  4. 30

Questions & Step-by-Step Solutions

In how many ways can 6 people be seated around a circular table?
Correct Answer: 120
  • Step 1: Understand that arranging people around a circular table is different from arranging them in a straight line.
  • Step 2: In a circular arrangement, one person's position can be fixed to avoid counting the same arrangement multiple times.
  • Step 3: Fix one person in one seat. This means we only need to arrange the remaining 5 people.
  • 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 there are 120 different ways to arrange 6 people around a circular table.
  • Circular Permutations – In circular arrangements, one position is fixed to account for rotations, leading to (n-1)! arrangements for n people.
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