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# how many different ways to seat 6 people around a circular

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Current Student
Joined: 31 Aug 2007
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how many different ways to seat 6 people around a circular [#permalink]

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01 Aug 2008, 13:56
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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, 16:11, edited 1 time in total.

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Intern
Joined: 28 May 2008
Posts: 7

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01 Aug 2008, 14:38
my guess 72
total ways = 5! = 120
pair together = 2*4! = 48

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Manager
Joined: 28 Apr 2008
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31 Oct 2008, 08:29
1
KUDOS
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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Manager
Joined: 28 Jul 2004
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Location: Melbourne
Schools: Yale SOM, Tuck, Ross, IESE, HEC, Johnson, Booth

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01 Nov 2008, 07:33
why does the permutation of n objects become (n-1)! in a circle?
_________________

kris

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Manager
Joined: 07 Jul 2007
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01 Dec 2008, 19:20
It is because if you take for example 3 elements in circle called A, B and C then there possible arrangements in circle are

ABC
CAB
BCA

These three arrangements in circle are same....if you arrage them in circle then you will realize how it is.

Kudos [?]: 35 [0], given: 0

Manager
Joined: 07 Jul 2007
Posts: 133

Kudos [?]: 35 [0], given: 0

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01 Dec 2008, 19:20
It is because if you take for example 3 elements in circle called A, B and C then there possible arrangements in circle are

ABC
CAB
BCA

These three arrangements in circle are same....if you arrage them in circle then you will realize how it is.

Kudos [?]: 35 [0], given: 0

Re: PS seating   [#permalink] 01 Dec 2008, 19:20
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