How many different ways can desserts be arranged on the circular tray if there are 4 desserts?

Here's how to figure out the number of arrangements for desserts on a circular tray:

Understanding Circular Permutations

Circular permutations are different from linear permutations because rotations of the same arrangement are considered the same.

* Example: Imagine four desserts: A, B, C, and D. The arrangements ABCD, BCDA, CDAB, and DABC are all considered the same because they are just rotations of each other.

The Calculation

1. Calculate the factorial: If the desserts were in a line, there would be 4! (4 factorial) ways to arrange them: 4 * 3 * 2 * 1 = 24.

2. Divide by the number of rotations: Since each arrangement has 4 rotations that are considered the same, we divide the factorial by 4.

3. The answer: 24 / 4 = 6

Therefore, there are 6 different ways to arrange 4 desserts on a circular tray.