# A circular permutation problem.

• Mar 24th 2012, 12:59 PM
serhanbener
A circular permutation problem.
There are 8 empty seats around a round table. A,B,C,D,E will sit
around the table. In how many ways they can sit around the table if
A and B must sit together?
• Mar 24th 2012, 01:14 PM
Plato
Re: A circular permutation problem.
Quote:

Originally Posted by serhanbener
There are 8 empty seats around a round table. A,B,C,D,E will sit
around the table. In how many ways they can sit around the table if
A and B must sit together?

Saying that A and B must sit together, I assume that means that A&B sit next each other/
In that case place them at the table together. That can be done two ways.
Now the table is ordered, there are six seats to permute three at a time.
• Mar 24th 2012, 10:05 PM
serhanbener
Re: A circular permutation problem.
How did you find "six seats to permute three at a time"?
This is a round table. There are 8 seats but we accept them 7 seats. There are 5 persons but we accept them as 4. AB can be ordered between themselves in 2!.
• Mar 25th 2012, 04:06 AM
Plato
Re: A circular permutation problem.
Quote:

Originally Posted by serhanbener
How did you find "six seats to permute three at a time"?
This is a round table. There are 8 seats but we accept them 7 seats. There are 5 persons but we accept them as 4. AB can be ordered between themselves in 2!.

Seat A at the table. Now it is no longer a 'round table', it is now ordered.
There are two places to seat B.
There are six places to seat C.
There are five places to seat D.
There are four places to seat E.
• Mar 25th 2012, 07:39 AM
serhanbener
Re: A circular permutation problem.
Why did you divide by 3!?
• Mar 25th 2012, 08:21 AM
Plato
Re: A circular permutation problem.
Quote:

Originally Posted by serhanbener
Why did you divide by 3!?

What part of reply #4 don't you understand?
• Mar 25th 2012, 09:40 AM
serhanbener
Re: A circular permutation problem.
We accept AB as one person. Now there are 6 chairs and 3 persons. 6 objects taken 3 at a time. Am I right?
• Mar 25th 2012, 09:50 AM
Plato
Re: A circular permutation problem.
Quote:

Originally Posted by serhanbener
We accept AB as one person. Now there are 6 chairs and 3 persons. 6 objects taken 3 at a time. Am I right?

You simply did not answer this question.
What part of reply #4 don't you understand?
We do not think of AB as one person.
We seat each of the five one at a time.
• Mar 25th 2012, 10:02 AM
serhanbener
Re: A circular permutation problem.
OK. This part: 6!/3!
• Mar 25th 2012, 10:06 AM
Plato
Re: A circular permutation problem.
Quote:

Originally Posted by serhanbener
OK. This part: 6!/3!

That is nowhere to be found is reply #4.