Question

A committee of 11 members sit at a round table. In how many ways can they be seated if the “President” and the “Secretary” choose to sit together.

• A. \(\frac{10!}{2!}\)
• B. \(\frac{9!}{2!}\)
• C. 9!x2!
• D. \(\frac{11!}{2!}\)

Answer 1

The Correct Option is C

To find the number of ways the committee members can be seated if the 'president' and 'secretary' choose to sit together, we can consider them as a single entity (president-secretary pair). This reduces the problem to arranging 10 entities (9 committee members + 1 president-secretary pair) around a round table. 

Now, the number of ways to arrange 10 entities around a round table is given by (10 - 1)!, which is 9!. This is because there are 10 seats available, but the arrangement can be rotated 10 times (each rotation giving the same arrangement), so we divide by 10. 

However, within the president-secretary pair, there are 2 arrangements: president-secretary and secretary-president. 

So, the total number of ways the committee can be seated with the president and secretary sitting together is 9! x 2!.