CAT 1997 — QA Question 8
Seating arrangementsEasy
Passage / Data
Answer the next 3 questions based on the following information.
There are 60 students in a class. These students are divided into three groups A, B and C of 15, 20 and 25 students each. The groups A and C are combined to form group D.
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?
Answer & solution
- A
9! × 2
2 × 8!
- C
2 × 7!
- D
None of these
Solution
If we consider the Chairman and the vice chairman as one set, we can see that 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. Hence, the required answer = 2 x 8!.