At a dinner party 5 people are to be seated around a circular table. Two sitting arrangements are considered different only when the positions of the people are different relative to each other.What is the total number of possible sitting arrangements or the group?

Options

A. a. 18
B. b. 50
C. c. 24
D. d. 36

Answer

To find the total number of possible seating arrangements for 5 people around a circular table, we can follow these steps:

### Step 1: Understand the Circular Arrangement Concept
In a circular arrangement, one position is usually fixed to avoid counting the same arrangement multiple times due to rotation. This is because rotating the entire arrangement does not create a new arrangement.

### Step 2: Use the Formula for Circular Permutations
For `n` distinct objects arranged in a circle, the number of arrangements is given by the formula:
\[ (n - 1)! \]
This is because we fix one person and arrange the remaining `n - 1` people around them.

### Step 3: Apply the Formula
In this case, we have 5 people:
- So, we will calculate:
\[ (5 - 1)! = 4! \]

### Step 4: Calculate 4!
Now we compute \( 4! \):
\[ 4! = 4 \times 3 \times 2 \times 1 = 24 \]

### Conclusion
Thus, the total number of possible seating arrangements for 5 people around a circular table is:
\[ \boxed{24} \]

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