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alex.gellatly GMAT Destroyer! Default Avatar
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GMAT PREP PS question Post Mon Apr 16, 2012 1:21 am
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    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 total number of different possible seating arrangements for the group?
    (A) 5
    (B) 10
    (C) 24
    (D) 32
    (E) 120

    Thanks in advanced

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    killer1387 GMAT Destroyer! Default Avatar
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    Post Mon Apr 16, 2012 1:36 am
    alex.gellatly 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 total number of different possible seating arrangements for the group?
    (A) 5
    (B) 10
    (C) 24
    (D) 32
    (E) 120

    Thanks in advanced
    Fix one guy,
    rest can be arranged in 4! ways
    hence answer is 4!= 24

    hence C

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    Anurag@Gurome GMAT Instructor
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    Post Mon Apr 16, 2012 3:50 am
    alex.gellatly 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 total number of different possible seating arrangements for the group?
    (A) 5
    (B) 10
    (C) 24
    (D) 32
    (E) 120

    Thanks in advanced
    For circular seating arrangement, the number of arrangements of n distinct objects in a row is given by n!.
    Number of arrangements of n distinct objects in a circle is given by (n - 1)!.

    So, in this the total number of different possible seating arrangements for the group = (5 - 1)! = 4! = 4 * 3 * 2 * 1 = 24 ways

    The correct answer is C.

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    niketdoshi123 Really wants to Beat The GMAT!
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    Post Mon Apr 16, 2012 3:59 am
    the answer should be (n-1)! where,
    n= total no. of people.
    This is only valid if people are to be seated around a circular table (all the seats are considered to be identical).
    so fix one guy's position and arrange others wrt him.
    hence in this case the ans is (n-1)!= (5-1)! = 24 option C

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    Post Mon Apr 16, 2012 4:01 am
    I discussed how to count circular permutations here:

    http://www.beatthegmat.com/seating-arrangement-t85488.html

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