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22 Aug 2013, 11:29
Kudos
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
75% (00:34) correct
25%
(01:23)
wrong
based on 353
sessions
History
Date
Time
Result
Not Attempted Yet
At a meeting, 6 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) 12
(B) 72
(C) 120
(D) 144
(E) 720
(A) 12
(B) 72
(C) 120
(D) 144
(E) 720
22 Aug 2013, 11:37
Kudos
Bookmarks
At a meeting, 6 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) 12
(B) 72
(C) 120
(D) 144
(E) 720
We have a case of circular arrangement.
The number of arrangements of n distinct objects in a row is given by \(n!\).
The number of arrangements of n distinct objects in a circle is given by \((n-1)!\).
From Gmat Club Math Book (combinatorics chapter):
"The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have:
\(R = \frac{n!}{n} = (n-1)!\)"
\((n-1)!=(6-1)!=120\)
Answer: C.
Questions about this concept to practice:
seven-men-and-seven-women-have-to-sit-around-a-circular-92402.html
a-group-of-four-women-and-three-men-have-tickets-for-seven-a-88604.html
the-number-of-ways-in-which-5-men-and-6-women-can-be-seated-94915.html
in-how-many-different-ways-can-4-ladies-and-4-gentlemen-be-102187.html
4-couples-are-seating-at-a-round-tables-how-many-ways-can-131048.html
at-a-party-5-people-are-to-be-seated-around-a-circular-104101.html
seven-family-members-are-seated-around-their-circular-dinner-102184.html
seven-men-and-seven-women-have-to-sit-around-a-circular-11473.html
a-group-of-8-friends-sit-together-in-a-circle-alice-betty-106928.html
seven-men-and-five-women-have-to-sit-around-a-circular-table-98185.html
a-group-of-8-friends-sit-together-in-a-circle-alice-betty-106928.html
find-the-number-of-ways-in-which-four-men-two-women-and-a-106919.html
gmat-club-monday-giveaway-155157.html (700+)
Hope it helps.
(A) 12
(B) 72
(C) 120
(D) 144
(E) 720
We have a case of circular arrangement.
The number of arrangements of n distinct objects in a row is given by \(n!\).
The number of arrangements of n distinct objects in a circle is given by \((n-1)!\).
From Gmat Club Math Book (combinatorics chapter):
"The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have:
\(R = \frac{n!}{n} = (n-1)!\)"
\((n-1)!=(6-1)!=120\)
Answer: C.
Questions about this concept to practice:
seven-men-and-seven-women-have-to-sit-around-a-circular-92402.html
a-group-of-four-women-and-three-men-have-tickets-for-seven-a-88604.html
the-number-of-ways-in-which-5-men-and-6-women-can-be-seated-94915.html
in-how-many-different-ways-can-4-ladies-and-4-gentlemen-be-102187.html
4-couples-are-seating-at-a-round-tables-how-many-ways-can-131048.html
at-a-party-5-people-are-to-be-seated-around-a-circular-104101.html
seven-family-members-are-seated-around-their-circular-dinner-102184.html
seven-men-and-seven-women-have-to-sit-around-a-circular-11473.html
a-group-of-8-friends-sit-together-in-a-circle-alice-betty-106928.html
seven-men-and-five-women-have-to-sit-around-a-circular-table-98185.html
a-group-of-8-friends-sit-together-in-a-circle-alice-betty-106928.html
find-the-number-of-ways-in-which-four-men-two-women-and-a-106919.html
gmat-club-monday-giveaway-155157.html (700+)
Hope it helps.
General Discussion
04 Oct 2023, 07:26
Kudos
Bookmarks
At a meeting, 6 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) 12
(B) 72
(C) 120
(D) 144
(E) 720
(A) 12
(B) 72
(C) 120
(D) 144
(E) 720
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