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

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

Options:

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

Correct Answer: 720

Solution: 

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

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

Practice Questions

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

Questions & Step-by-Step Solutions

In how many ways can 6 people be seated in 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 when arranging people in a circle, one person's position can be fixed to avoid counting the same arrangement multiple times.
  • Step 3: Fix one person in a seat. This means you 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 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, reducing the total arrangements by one factorial.
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