Val911 wrote:Please help me out with the following GMAT Prep Question:
At a dinner party 5 people are to be seated around a circular table. Two sitting arrangements are considered different only when the positions of the people are different relative to each other.What is the total number of possible sitting arrangements or the group?
A)5
B)10
C)24
D)32
E)120
Let's say that the 5 people are ABCDE.
If we count the number of ways to arrange these elements IN A LINE, the following qualify as different arrangements.
ABCDE
BCDEA
CDEAB
DEABD
EABCD
But put around a table, all of the above qualify as only ONE arrangement, because the clockwise order in each case is THE SAME: A-B-C-D-E.
In all of the above:
B is directly to the right of A
C is directly to the right of B
D is directly to the right of C
E is directly to the right of D.
A is directly to the right of E.
Thus:
When N people are arranged in a circle, where the first person sits doesn't matter.
What we need to count is the number of ways to arrange the other N-1 people RELATIVE to the first person.
The result is the following formula:
The number of ways to arrange N people around a circular table = (N-1)!.
Thus, the number of ways to arrange 5 in a circle = (5-1)! = 4! = 24.
The correct answer is
C.
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