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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 the vice chairman and a director?

  1. 9! × 2
  2. 2 × 7!
  3. 2 × 8!
  4. 2 × 6!

Answer

If you consider the Chairman and the vice chairman as one set, this set can fit 8 slots in between the 8 directors. Hence, this can be done in 8! ways.

Between themselves, the chairman and the vice chairman can be arranged in 2 ways.

So, total number of ways are 2 × 8!

The correct option is C.