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M01, Q24

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Current Student
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Joined: 28 Dec 2011
Posts: 9
Location: United States (IL)
Concentration: International Business, Nonprofit
GMAT 1: 750 Q48 V44
GPA: 2.84
WE: Military Officer (Military & Defense)
Followers: 0

Kudos [?]: 6 [0], given: 1

M01, Q24 [#permalink] New post 29 Dec 2011, 14:55
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

100% (01:01) correct 0% (00:00) wrong based on 0 sessions
If 5 noble knights are to be seated at a round table, then how many different ways can they be seated?


120
96
60
35
24




Fix a knight in a spot to arrange the rest. The formula is (5-1)!, or 4!

The correct answer is E.

Why is the answer 4! and not (5!)?

I can't wrap my head around that.

When I see 5 people, 5 empty spots, I automatically think - ok

5x4x3x2x1 = 5!

1st seat can have any of the 5
2nd seat will have one of the remaining 4...etc etc etc.

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Magoosh GMAT Instructor
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Kudos [?]: 1984 [2] , given: 29

Re: M01, Q24 [#permalink] New post 29 Dec 2011, 15:56
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Expert's post
Great question! I'm happy to help!

You are SO close --- in fact, if we were seating these five knights in a straight line (for example, on a long bench), then the number of arrangements would be 5! = 120

Here's what's diabolically tricky about this question: they're at a ROUND table.

Suppose the 5 knights are A, B, C, D, and E.

If they sit as ABCDE vs.CDEAB on a bench, those are two very different arrangements. At a round table though (assuming there are five seats equally spaced around the table), those two are identical arrangements: each knight has the same two neighbors on his same respective sides. These two seating plans are shown in the diagram below.

So, really the question is: let's say A sits in a seat --- that could be any seat, since they are all symmetrical. Once A has sat, there are 4! ways for the other four knights to fill those other four spaces. Thus, only 4! possibilities.

I hope that was clear and helpful. Please let me know if you have any questions.

Mike :)
Attachments

knights' seating plans.PNG
knights' seating plans.PNG [ 25.5 KiB | Viewed 555 times ]


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Mike McGarry
Magoosh Test Prep

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Current Student
avatar
Joined: 28 Dec 2011
Posts: 9
Location: United States (IL)
Concentration: International Business, Nonprofit
GMAT 1: 750 Q48 V44
GPA: 2.84
WE: Military Officer (Military & Defense)
Followers: 0

Kudos [?]: 6 [0], given: 1

Re: M01, Q24 [#permalink] New post 29 Dec 2011, 19:19
Once I posted, the similar threads thing on the bottom popped up and I found the answer. But your explanation was very clear and concise. Thank you.
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"Never doubt that a small group of thoughtful, committed citizens can change the world. Indeed, it's the only thing that ever has" - Margaret Mead

Re: M01, Q24   [#permalink] 29 Dec 2011, 19:19
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