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Alice, Bob, Cindy, Daren, Eddie, Farrell sit on chairs around a round
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MathRevolution
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Alice, Bob, Cindy, Daren, Eddie, Farrell sit on chairs around a round [#permalink] New post  29 Apr 2019, 17:31
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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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chetan2u
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Re: Alice, Bob, Cindy, Daren, Eddie, Farrell sit on chairs around a round [#permalink] New post  30 Apr 2019, 03:47
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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
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Re: Alice, Bob, Cindy, Daren, Eddie, Farrell sit on chairs around a round [#permalink] New post  30 Apr 2019, 07:56
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.

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Re: Alice, Bob, Cindy, Daren, Eddie, Farrell sit on chairs around a round [#permalink] New post  30 Apr 2019, 23:48
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=>

Attachment:
429.png
429.png [ 16.12 KiB | Viewed 943 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
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Re: Alice, Bob, Cindy, Daren, Eddie, Farrell sit on chairs around a round [#permalink] New post  02 May 2019, 06:27
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.

Therefore, C is the answer.
Answer: C



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

then answer should be 48

Could you help on this doubt ….
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Re: Alice, Bob, Cindy, Daren, Eddie, Farrell sit on chairs around a round [#permalink] New post  02 May 2019, 07:03
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.

Therefore, C is the answer.
Answer: C



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

then answer should be 48

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
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Re: Alice, Bob, Cindy, Daren, Eddie, Farrell sit on chairs around a round [#permalink] New post  03 May 2019, 08:05
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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.

Therefore, C is the answer.
Answer: C



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

then answer should be 48

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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Re: Alice, Bob, Cindy, Daren, Eddie, Farrell sit on chairs around a round [#permalink] New post  15 May 2019, 18:57
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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] New post  15 May 2019, 19:26
Yes it is the right approach, as the two positions are fixed, the four persons can sit in 4! ways.
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