In a conference hall, 13 chairs are arranged around a round table. Find the possible ways that 13 people can occupy the seats

To find the number of ways in which 13 people can occupy 13 chairs arranged around a round table, we need to consider the concept of circular permutations.

1. ### Break Down the Problem

In circular permutations, one position is fixed to eliminate the indistinguishable arrangements that come from the rotation of the entire group around the table. Thus, if we have $n$ people, the number of ways to arrange them around a circular table is given by $(n-1)!$.

2. ### Relevant Concepts

For $n = 13$:

• The formula for circular permutations is: $(n-1)!$

3. ### Analysis and Detail

1. Calculate $(13 - 1)!$:

   • This simplifies to $12!$.

2. Calculate $12!$: $12! = 12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 479001600$

4. ### Verify and Summarize

To summarize, fixing one person's position and calculating the arrangements of the remaining 12 gives us $12! = 479001600$. Therefore, the count of unique seating arrangements for the 13 people around the table is confirmed as correct.

Final Answer

The possible ways that 13 people can occupy the seats around the table is $479001600$.