# Thread: A circular permutation problem.

1. ## 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?

2. ## Re: A circular permutation problem.

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.
What answer do you get?

3. ## 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!.

4. ## Re: A circular permutation problem.

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.

5. ## Re: A circular permutation problem.

Why did you divide by 3!?

6. ## Re: A circular permutation problem.

Originally Posted by serhanbener
Why did you divide by 3!?
What part of reply #4 don't you understand?

7. ## 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?

8. ## Re: A circular permutation problem.

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.

9. ## Re: A circular permutation problem.

OK. This part: 6!/3!

10. ## Re: A circular permutation problem.

Originally Posted by serhanbener
OK. This part: 6!/3!
That is nowhere to be found is reply #4.
Did you even read reply #4?

11. ## Re: A circular permutation problem.

Many Thanks Plato. Solution is:2!.6!/3!=240. I was asking about "6!/3!". But I understood it now.