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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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/Quote:
Originally Posted by serhanbener
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?
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.Quote:
Originally Posted by serhanbener
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.
Why did you divide by 3!?
What part of reply #4 don't you understand?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.Quote:
Originally Posted by serhanbener
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.
OK. This part: 6!/3!
That is nowhere to be found is reply #4.Quote:
Originally Posted by serhanbener
Did you even read reply #4?
Many Thanks Plato. Solution is:2!.6!/3!=240. I was asking about "6!/3!". But I understood it now.