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In how many ways can 5 persons be seated around a circular

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huda
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In how many ways can 5 persons be seated around a circular [#permalink] New post   12 Aug 2019, 06:44
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In how many ways can 5 persons be seated around a circular table?

A.\(5\)
B.\(24\)
C.\(25\)
D.\(30\)
E.\(120\)
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B
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huda
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Re: In how many ways can 5 persons be seated around a circular [#permalink] New post   12 Aug 2019, 06:44
huda wrote:
In how many ways can 5 persons be seated around a circular table?

A.\(5\)
B.\(24\)
C.\(25\)
D.\(30\)
E.\(120\)


NEED EXPLANATION
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Re: In how many ways can 5 persons be seated around a circular [#permalink] New post   12 Aug 2019, 07:38
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Expert Reply
5 persons can be seated around a round table in (5 - 1)! = 4! = 24 ways.

B is the answer
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nileshk
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Re: In how many ways can 5 persons be seated around a circular [#permalink] New post   16 Aug 2019, 02:34
Carcass wrote:
5 persons can be seated around a round table in (5 - 1)! = 4! = 24 ways.

B is the answer



Why (5-1)!? Is it not 5!?
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smartchin77
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Re: In how many ways can 5 persons be seated around a circular [#permalink] New post   16 Aug 2019, 02:52
1
nileshk wrote:
Carcass wrote:
5 persons can be seated around a round table in (5 - 1)! = 4! = 24 ways.

B is the answer



Why (5-1)!? Is it not 5!?


https://www.askiitians.com/iit-jee-alge ... tions.aspx
They have explained it well
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nileshk
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Re: In how many ways can 5 persons be seated around a circular [#permalink] New post   16 Aug 2019, 06:45
smartchin77 wrote:
nileshk wrote:
Carcass wrote:
5 persons can be seated around a round table in (5 - 1)! = 4! = 24 ways.

B is the answer



Why (5-1)!? Is it not 5!?


https://www.askiitians.com/iit-jee-alge ... tions.aspx
They have explained it well


Thanks.
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Re: In how many ways can 5 persons be seated around a circular [#permalink] New post   08 Aug 2021, 10:18
1
Circular arrangement concept! Why it's really (n-1) factorial?
circular table having 5 seats, we have 5 people to occupy.
The first guy has no unique positions in a circle all 5 are the same to him, once the first guy is filled in circular arrangement, with him being the reference point we have 4 unique positions for others hence (n-1) !

what about the rectangular table? the first guy has 3 positions(assuming 6 total sitting positions 2 along sidelength and 1 each along the width), once the first guy occupies anyone then Normal arrangement begins.
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