TestPrep probability

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moneyman: Master | Next Rank: 500 Posts; Posts: 468; Joined: Sat Mar 03, 2007 10:17 pm; Thanked: 5 times

by moneyman » Mon Feb 25, 2008 7:50 am

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 froup?

5
10
24
32
120

OA is C

Maxx

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Source: Beat The GMAT — Problem Solving | Mon Feb 25, 2008 7:50 am

torontogmat.com: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Mon Feb 11, 2008 11:34 am; Location: Toronto; Thanked: 7 times

by torontogmat.com » Mon Feb 25, 2008 9:24 am

Since the *relative* positions are what matters, it is irrelevant where the first person sits. Then there are 4 different choices for the 2nd person. Wherever he sits, there will be 3 choices for the next person, and wherever that person sits, there will be 2 choices for the next person. There will only be one seat left for the last person.

4 x 3 x 2 x 1 = 24. As you can see, (n-1)! will be the solution for the general case.

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