In how many ways can 7 different objects be arranged in a circle?

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Question: In how many ways can 7 different objects be arranged in a circle?

Options:

Correct Answer: 5040

Solution:

The number of arrangements in a circle is (n-1)! = 6! = 720.

In how many ways can 7 different objects be arranged in a circle?

In how many ways can 7 different objects be arranged in a circle?

Step 1: Understand that we have 7 different objects to arrange.
Step 2: Know that when arranging objects in a circle, one object can be fixed to avoid counting the same arrangement multiple times.
Step 3: Since we fix one object, we only need to arrange the remaining 6 objects.
Step 4: Calculate the number of arrangements for the 6 objects, which is done using the factorial of 6, written as 6!.
Step 5: Calculate 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720.
Step 6: Conclude that the total number of ways to arrange 7 different objects in a circle is 720.

Circular Permutations – In circular arrangements, one object is fixed to account for rotations, leading to (n-1)! arrangements.