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In how many ways can 6 people be seated at a round table?

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Question: In how many ways can 6 people be seated at a round table?

Options:

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

Correct Answer: 120

Solution: 

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

In how many ways can 6 people be seated at a round table?

Practice Questions

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

Questions & Step-by-Step Solutions

In how many ways can 6 people be seated at a round table?
Correct Answer: 120
  • 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 if we fix one person in one seat, we can arrange the remaining people around them.
  • Step 3: Since we have fixed one person, we now have 5 people left to arrange.
  • Step 4: The number of ways to arrange 5 people in a line is calculated using factorial, which is written as 5!.
  • Step 5: Calculate 5! (5 factorial), which means 5 x 4 x 3 x 2 x 1 = 120.
  • Step 6: Conclude that the total number of ways to arrange 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 for n people.
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