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GMAT Question of the Day - Problem Solving - Combinatorics

How many unique ways can 7 people be arranged around a circular table (The same relative arrangement does not count as unique)?

A. 7!

B. 6!

C. 5!

D. 7!/5!

E. 7!/4!

Answer Show

GMAT Question of the Day Solution

Most GMAT combinations/permutations questions are not difficult but many GMAT tutoring students are worried about these topics. Most likely you won't see many of these on your GMAT. But still it's worth knowing the basics. This GMAT question of the day focuses on a specific type of permutation: the circular arrangement.

Circular arrangements are different than straight line arrangements in that the question will generally specify that if the same relative positions are maintained around the circle then the arrangement has not changed. Meaning if you're sitting in between Bill and Bob and then everyone moves one chair to the left and you are still between Bill and Bob that's not a new arrangement. How do you take this into account? Simple: subtract one from the total and then take the factorial. In this case (7-1)! or 6!.

GMAT Question of the Day Problem Solving Combinatorics Explanation Diagram

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