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

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

chetan2u · Answer

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

sach24x7 · Answer

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

MathRevolution · Answer

=> 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

m1033512 · Answer

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 ….

ArupRS · Answer

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

MathRevolution · Answer

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.

Abhishek292kumar · Answer

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?

kinvestor · Answer

Yes it is the right approach, as the two positions are fixed, the four persons can sit in 4! ways.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards