Question

If eleven members of a committee sit at a round table so that the President and Secretary always sit together, then the number of arrangements is?

• A. $10!\times 2$
• B. $10!$
• C. $9!\times 2$
• D. None of these

Answer 1

The correct option is C

$9!\times 2$

Finding the number of arrangements:

Considering the president and secretary as one member, we have now $10$ members in all.

These $10$ members can be seated around the circular table in $(10–1)!=9!$ ways.

Also the president and secretary can seat themselves in $2!$ways $PS$ or $SP$

∴ Required number of ways of seating = $9!\times 2!$

Hence, the correct answer is option C