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How many ways can 6 people be arranged in a circle?

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Question: How many ways can 6 people be arranged in a circle?

Options:

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

Correct Answer: 720

Solution: 

The number of arrangements in a circle is (n-1)! = (6-1)! = 5! = 120.

How many ways can 6 people be arranged in a circle?

Practice Questions

Q1
How many ways can 6 people be arranged in a circle?
  1. 720
  2. 120
  3. 60
  4. 30

Questions & Step-by-Step Solutions

How many ways can 6 people be arranged in a circle?
Correct Answer: 120
  • Step 1: Understand that arranging people in a circle is different from arranging them in a line.
  • Step 2: When arranging in a circle, one person's position is fixed to avoid counting the same arrangement multiple times.
  • Step 3: For 6 people, we can fix one person in place, leaving us with 5 people to arrange.
  • Step 4: The number of ways to arrange these 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: Therefore, the total number of ways to arrange 6 people in a circle is 120.
  • Circular Permutations – In circular arrangements, one position is fixed to account for rotations, leading to (n-1)! arrangements.
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