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# 6 guys (let's call them ABCDEF) sit around a circular table. If the AB

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CEO
Joined: 21 Jan 2007
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Location: New York City
6 guys (let's call them ABCDEF) sit around a circular table. If the AB  [#permalink]

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13 Mar 2008, 08:43
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6 guys (let's call them ABCDEF) sit around a circular table. If the AB must always sit together, and C must face the door, how many arrangements are possible? please explain your work...
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Re: 6 guys (let's call them ABCDEF) sit around a circular table. If the AB  [#permalink]

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13 Mar 2008, 09:19
48

1. "C must face the door" - the condition fixes circular shifts.
2. "the AB must always sit together" - we can consider AB one object, but count it twice as AB and BA .
3. We have 4 objects (3 guys and one couple ): 4P4=4!=24
4. finally, N=24*2=48
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Re: 6 guys (let's call them ABCDEF) sit around a circular table. If the AB  [#permalink]

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13 Mar 2008, 10:32
48 it is

It looks like a circular permutation problem, but is a liner instead.
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Re: 6 guys (let's call them ABCDEF) sit around a circular table. If the AB  [#permalink]

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20 Jan 2011, 08:49
Is it linear because the one guy must face the door?
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Re: 6 guys (let's call them ABCDEF) sit around a circular table. If the AB  [#permalink]

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08 Sep 2018, 03:38
walker wrote:
48

1. "C must face the door" - the condition fixes circular shifts.
2. "the AB must always sit together" - we can consider AB one object, but count it twice as AB and BA .
3. We have 4 objects (3 guys and one couple ): 4P4=4!=24
4. finally, N=24*2=48

IF C facing the door fixes circular shifts , then shouldn't we have 5!*2

{AB} {C}{D}{E}{F} that's 5!2!

Unless we are arranging this group circularly. 4!2!
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Re: 6 guys (let's call them ABCDEF) sit around a circular table. If the AB   [#permalink] 08 Sep 2018, 03:38
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