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how many different ways to seat 6 people around a circular

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how many different ways to seat 6 people around a circular [#permalink] New post 01 Aug 2008, 12:56
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how many different ways to seat 6 people around a circular table if 2 of the 6 refuse to sit adjacent to one another?
96?

hmm agree 72

Last edited by young_gun on 01 Aug 2008, 15:11, edited 1 time in total.
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Re: PS seating [#permalink] New post 01 Aug 2008, 13:38
my guess 72
total ways = 5! = 120
pair together = 2*4! = 48
answer = 120-48 = 72
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Re: PS seating [#permalink] New post 31 Oct 2008, 07:29
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I think it's 72

6 people can seated in 5! ways around a round table.

if 2 cant sit in ajacent seats- one of then has only 3c1 seats and te rest have 4! wayr to be seated.

we are left with 3*4!= 72 ways
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Re: PS seating [#permalink] New post 01 Nov 2008, 06:33
why does the permutation of n objects become (n-1)! in a circle?
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Re: PS seating [#permalink] New post 01 Dec 2008, 18:20
It is because if you take for example 3 elements in circle called A, B and C then there possible arrangements in circle are
only 2 instead of 6.

ABC
CAB
BCA

These three arrangements in circle are same....if you arrage them in circle then you will realize how it is.
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Re: PS seating [#permalink] New post 01 Dec 2008, 18:20
It is because if you take for example 3 elements in circle called A, B and C then there possible arrangements in circle are
only 2 instead of 6.

ABC
CAB
BCA

These three arrangements in circle are same....if you arrage them in circle then you will realize how it is.
Re: PS seating   [#permalink] 01 Dec 2008, 18:20
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