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# Alice, Bob, Cindy, Daren, Eddie, Farrell sit on chairs around a round

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Math Revolution GMAT Instructor
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Alice, Bob, Cindy, Daren, Eddie, Farrell sit on chairs around a round  [#permalink]

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29 Apr 2019, 18:31
00:00

Difficulty:

35% (medium)

Question Stats:

63% (01:13) correct 38% (01:26) wrong based on 72 sessions

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[GMAT math practice question]

Alice, Bob, Cindy, Daren, Eddie, Farrell sit on chairs around a round table. Alice sits opposite Farrell. How many seating arrangements are possible?

A. 2
B. 6
C. 24
D. 120
E. 720

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 7686 Re: Alice, Bob, Cindy, Daren, Eddie, Farrell sit on chairs around a round [#permalink] ### Show Tags 30 Apr 2019, 04:47 MathRevolution wrote: [GMAT math practice question] Alice, Bob, Cindy, Daren, Eddie, Farrell sit on chairs around a round table. Alice sits opposite Farrell. How many seating arrangements are possible? A. 2 B. 6 C. 24 D. 120 E. 720 So, we have 6 person. First we fix the seat of Alice, and, so the seat of Farrell too gets fixed automatically. Now we have 4 seats for 4 different people, and these can be occupied in 4! or 24 ways C _________________ Manager Status: Don't Give Up! Joined: 15 Aug 2014 Posts: 97 Location: India Concentration: Operations, General Management GMAT Date: 04-25-2015 WE: Engineering (Manufacturing) Re: Alice, Bob, Cindy, Daren, Eddie, Farrell sit on chairs around a round [#permalink] ### Show Tags 30 Apr 2019, 08:56 In circular arrangements if there is no constraints then arrangements are (n-1)! But if we fix position of ALICE AND FARELL then remaining 4 positions will be taken by 4 people in 4! ways. Posted from my mobile device _________________ - Sachin -If you like my explanation then please click "Kudos" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7372 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Alice, Bob, Cindy, Daren, Eddie, Farrell sit on chairs around a round [#permalink] ### Show Tags 01 May 2019, 00:48 => Attachment: 429.png [ 16.12 KiB | Viewed 493 times ] First, place Alice and Farrell in opposite chairs as shown above (there is only one way to do this as the table is round). Next, arrange the four remaining people in $$4! = 24$$ ways. Therefore, C is the answer. Answer: C _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Re: Alice, Bob, Cindy, Daren, Eddie, Farrell sit on chairs around a round  [#permalink]

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02 May 2019, 07:27
MathRevolution wrote:
=>

Attachment:
429.png

First, place Alice and Farrell in opposite chairs as shown above (there is only one way to do this as the table is round).
Next, arrange the four remaining people in $$4! = 24$$ ways.

but Alice and Farrel can change their positions in 2! ways ( they exchange their seats and it will be a different arrangement)

Could you help on this doubt ….
Manager
Joined: 23 Jan 2018
Posts: 166
Location: India
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Re: Alice, Bob, Cindy, Daren, Eddie, Farrell sit on chairs around a round  [#permalink]

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02 May 2019, 08:03
m1033512 wrote:
MathRevolution wrote:
=>

Attachment:
429.png

First, place Alice and Farrell in opposite chairs as shown above (there is only one way to do this as the table is round).
Next, arrange the four remaining people in $$4! = 24$$ ways.

but Alice and Farrel can change their positions in 2! ways ( they exchange their seats and it will be a different arrangement)

Could you help on this doubt ….

I also have the same doubt. Also, aren't we also ignoring the fact that A & F can have 3 position all together.

Regards,
Arup
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7372
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Alice, Bob, Cindy, Daren, Eddie, Farrell sit on chairs around a round  [#permalink]

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03 May 2019, 09:05
ArupRS wrote:
m1033512 wrote:
MathRevolution wrote:
=>

Attachment:
429.png

First, place Alice and Farrell in opposite chairs as shown above (there is only one way to do this as the table is round).
Next, arrange the four remaining people in $$4! = 24$$ ways.

but Alice and Farrel can change their positions in 2! ways ( they exchange their seats and it will be a different arrangement)

Could you help on this doubt ….

I also have the same doubt. Also, aren't we also ignoring the fact that A & F can have 3 position all together.

Regards,
Arup

Before Alice and Farrell take seates, we don't know which seat is first and which seat is last.
After Alice and Farrell take seates, we can figure out the rest of seats and 4! = 24 is the number of arrangemnets.
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Intern
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Re: Alice, Bob, Cindy, Daren, Eddie, Farrell sit on chairs around a round  [#permalink]

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15 May 2019, 19:57
1
MathRevolution wrote:

Before Alice and Farrell take seates, we don't know which seat is first and which seat is last.
After Alice and Farrell take seates, we can figure out the rest of seats and 4! = 24 is the number of arrangemnets.

The number of ways sitting in round table is $$(n-1)!$$ where n is number of people.
Here we have 6 people in which A and F position is fixed so can be treated a one unit.
Therefore we just have to find the ways for 5 people to sit.
So $$(5-1)! = 4! = 24$$

Is this the right approach?
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Re: Alice, Bob, Cindy, Daren, Eddie, Farrell sit on chairs around a round  [#permalink]

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15 May 2019, 20:26
Yes it is the right approach, as the two positions are fixed, the four persons can sit in 4! ways.
Re: Alice, Bob, Cindy, Daren, Eddie, Farrell sit on chairs around a round   [#permalink] 15 May 2019, 20:26
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