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

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.