Question

Five friends are sitting in a circular arrangement. In how many ways can they be seated?

• A. 24
• B. 120
• C. 6
• D. 146

Hint:

When arranging people in a circular arrangement, use the formula \( (n - 1)! \) to find the number of ways to arrange them.

Answer 1

The Correct Option is A

In a circular arrangement, the number of ways to arrange \( n \) people is \( (n - 1)! \). This is because when arranging people in a circle, one person can be fixed, and the remaining \( n - 1 \) people can be arranged around them.
For 5 people, the number of ways to arrange them in a circle is: \[ (5 - 1)! = 4! = 4 \times 3 \times 2 \times 1 = 24 \] Thus, the number of ways the 5 friends can be seated in a circular arrangement is 24. Therefore, the correct answer is (1) 24.