Re: Permutations in a circle

Re: Permutations in a circle

Thanks soroban, but why are the engineers seated down first? Is it possible to sit the 9 councillors down then only the engineers?

Re: Permutations in a circle

Dear Soroban,

When the first engineer can sit in any chair, means he has 12 chairs in his choice is it not? or at least 3 chairs in his choice. Kindly explain me.

Re: Permutations in a circle

Quote:

Originally Posted by

**arangu1508** Dear Soroban,

When the first engineer can sit in any chair, means he has 12 chairs in his choice is it not? or at least 3 chairs in his choice. Kindly explain me.

The first engineer can sit in any 3 chairs, the next engineer 2 chairs, the last engineer can only sit in 1 chair

Re: Permutations in a circle

Then it becomes 3!. How come 2! ?

Re: Permutations in a circle

Quote:

Originally Posted by

**arangu1508** Then it becomes 3!. How come 2! ?

Consider an empty table. Put three chairs there.

Now seat the three engineers. Using *circular permutations** that can be done in ways.

At this point the table is *ordered*. Place three chairs between each of the engineers. Now there ways to seat the councilors.

**circular permutations*: there are ways to arrange *n* different objects in a circle.

Re: Permutations in a circle

thank you. Understood the concept now.(Giggle)

Re: Permutations in a circle

Quote:

Originally Posted by

**Plato** Consider an empty table. Put three chairs there.

Now seat the three engineers. Using

*circular permutations** that can be done in

ways.

At this point the table is

*ordered*. Place three chairs between each of the engineers. Now there

ways to seat the councilors.

*

*circular permutations*: there are

ways to arrange

*n* different objects in a circle.

this might be counterintuitive, but what happens if you decide to seat the councillors first? then the engineers?

Re: Permutations in a circle

Quote:

Originally Posted by

**aonin** this might be counterintuitive, but what happens if you decide to seat the councillors first? then the engineers?

One could do that. But it makes the explanation more difficult.

With three at the table, there is only one way to add nine more chairs in the required way.

But with nine already at the table how ways are there to add three more chairs in the required way?

Each engineer is between two councilors in the first way,

But the same cannot be said of the councilors.

We look for the least complicated way of modeling.