gdshamain wrote:At a dinner party, 5 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the number of different seating arrangements for the group?
A) 5
B) 10
C) 24
D) 32
E) 120
In a CIRCULAR arrangement, the first person seated is irrelevant.
Our job is to count the number of ways to arrange the REMAINING PEOPLE relative to the first person seated.
In the problem above:
Once 1 of the 5 people is seated, the number of ways to arrange the remaining 4 people = 4! = 24.
The correct answer is
C.
For those who like formulas:
The number of ways to arrange n elements in a circle = (n-1)!.
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