GRE® Permutation Practice

Concept: Circular Permutation

This sample GRE quant practice question is a permutation combination problem solving question. Concept tested is rearranging objects around a circle with a constraint.

Question: 8 directors, the vice chairman and the chairman are to be seated around a circular table. If the chairman should sit between a director and the vice chairman, in how many ways can they be seated?

  1. 9!
  2. 7! * 2
  3. 9! * 2
  4. 8! * 2
  5. 8!

Video Explanation

Scroll down for explanatory answer text

Explanatory Answer

Use these hints to get the answer

  1. Consider the possibilities where the chairman will be seated in between the vice chairman and a director.
  2. Permute the group around a circular table after considering the seating constraint.

Step 1: Address the constraint that the chairman has to be flanked by a director and the vice chairman.

Essentially, the constraint boils down to seating the chairman and the vice chairman next to each other because there will definitely be a director on the other side of the chairman.

Consider the chairman and vice chairman as one unit.

The chairman and the vice chairman can be reordered within that unit in 2! ways.

We have to seat 8 directors and a unit comprising the chairman and vice chairman i.e., nine units around a circular table.

Step 2: Re arrangement around a circular table - circular permutation

n objects can be permuted around a table in (n - 1)! ways.

So, 9 people viz., 8 directors and a unit comprising chairman and vice chairman can be permuted around a circular table in (9 - 1)! = 8! ways.

Total number of outcomes = number of ways of reordering the chairman and vice chairman within the unit * number of ways permuting the group around the table.

= 8! * 2 ways.

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