Question

In how many ways can eight directors, the vice chairman and chairman of a firm be seated at a round table, if the chairman has to sit between the vice chairman and a director?

• A. $9! \times 2$
• B. $2 \times 8!$
• C. $2 \times 7!$
• D. None of these

Hint:

In circular arrangements with fixed positions, treat one seat as fixed to avoid rotational duplicates.

Answer 1

The Correct Option is B

Fix the chairman’s position. Vice chairman can be on either side (2 ways). Remaining 8 directors can be arranged in $8!$ ways around the table. Therefore, total arrangements = $2 \times 8!$.