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23 Apr 2008, 18:46
Kudos
Bookmarks
Can someone explain this problem?
At a 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
I suck at probability and have no clue how to solve. Any tips?
At a 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
I suck at probability and have no clue how to solve. Any tips?
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
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23 Apr 2008, 21:20
Kudos
Bookmarks
If there are n people or objects then in circular combination they can be organised in (n-1)! ways.
So (5-1)! = 4! = 24
Now coming to "Two seating arrangements are considered different only when the positions of the people are different relative to each other." This part you can say is additional information that explains that yes we are using circular combination and nothing else. Consider case 1 person sits at seat A, 2nd on B, 3rd on C, 4th on D, and 5th on E. Now move each person by 1 that mean, 1st one on B, 2nd one of C and so on. In both the case all the person are sitting in same position relative to each other although they have moved their seats but there position relative to each other is same. So in effect you can fix one person and move all the other person, thereby fixing of one person bring (n-1).
So (5-1)! = 4! = 24
Now coming to "Two seating arrangements are considered different only when the positions of the people are different relative to each other." This part you can say is additional information that explains that yes we are using circular combination and nothing else. Consider case 1 person sits at seat A, 2nd on B, 3rd on C, 4th on D, and 5th on E. Now move each person by 1 that mean, 1st one on B, 2nd one of C and so on. In both the case all the person are sitting in same position relative to each other although they have moved their seats but there position relative to each other is same. So in effect you can fix one person and move all the other person, thereby fixing of one person bring (n-1).
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
