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?

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- Mar 24th 2012, 01:59 PMserhanbenerA 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, 02:14 PMPlatoRe: A circular permutation problem.
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? - Mar 24th 2012, 11:05 PMserhanbenerRe: 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, 05:06 AMPlatoRe: A circular permutation problem.
- Mar 25th 2012, 08:39 AMserhanbenerRe: A circular permutation problem.
Why did you divide by 3!?

- Mar 25th 2012, 09:21 AMPlatoRe: A circular permutation problem.
- Mar 25th 2012, 10:40 AMserhanbenerRe: 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, 10:50 AMPlatoRe: A circular permutation problem.
- Mar 25th 2012, 11:02 AMserhanbenerRe: A circular permutation problem.
OK. This part: 6!/3!

- Mar 25th 2012, 11:06 AMPlatoRe: A circular permutation problem.
- Mar 25th 2012, 11:16 AMserhanbenerRe: A circular permutation problem.
Many Thanks Plato. Solution is:2!.6!/3!=240. I was asking about "6!/3!". But I understood it now.