The Chief Minister Calls a meeting of 12b officers. In how ways can they be seated at a round table?A.12!B.11!C.13!D.10!

1. Break Down the Problem

To determine the number of ways to seat 12 officers at a round table, we note that seating arrangements in a circle are counted differently than in a straight line. When seating $n$ people at a round table, the number of distinct arrangements is given by $(n-1)!$ because one position can be fixed to eliminate identical rotations.

2. Relevant Concepts

For $n = 12$:

• The formula for the number of circular permutations is: $(n-1)! = (12-1)! = 11!$

3. Analysis and Detail

• Fix one officer in one seat (to account for circular arrangement).
• Arrange the remaining $n-1$ officers around the table.
• Therefore, the total arrangements will be $11!$.

4. Verify and Summarize

By fixing one officer, we convert the problem to arranging 11 officers in a straight line, confirming our calculation.

Final Answer

The number of ways to seat the officers at a round table is $11!$. Thus, the answer is B. 11!