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In how many ways can 6 ppl be seated in a circle if 2 ppl

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In how many ways can 6 ppl be seated in a circle if 2 ppl [#permalink] New post 09 Oct 2003, 15:43
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In how many ways can 6 ppl be seated in a circle if 2 ppl are always separated?
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Re: PS : Probability ( Circular arrangement) [#permalink] New post 09 Oct 2003, 16:03
5! - 4!

6 people can be arranged in a circle in 5! ways

Considering the 2 people that need to be away as a single person, we can get the combinations that the two of them are together = 4!

So, answer = 6! - 4! = 96 (if the order does not matter)
= 48 (if order does matter)

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Re: PS : Probability ( Circular arrangement) [#permalink] New post 09 Oct 2003, 16:12
amarsesh wrote:

5! - 4!
6 people can be arranged in a circle in 5! ways.
Considering the 2 people that need to be away as a single person, we can get the combinations that the two of them are together = 4!
So, answer = 6! - 4! = 96 (if the order does not matter)
= 48 (if order does matter)
Amar.


Did you get it backwards. If order matters, the answer is 96.

Dont you think that in arrangements , Order always matters , unless specified

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Re: PS : Probability ( Circular arrangement) [#permalink] New post 09 Oct 2003, 17:08
Sorry. Yes, you are right. I was hungry and wanted to finish typing it up. So, that was a side-effect of my hunger.

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Re: PS : Probability ( Circular arrangement) [#permalink] New post 01 Dec 2003, 20:40
i think we got this wrong

should this be 5! - 4! * 2! = 72

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Re: PS : Probability ( Circular arrangement) [#permalink] New post 01 Dec 2003, 23:03
praetorian123 wrote:
In how many ways can 6 ppl be seated in a circle if 2 ppl are always separated?


There are 5! ways for 6 people to sit in a circle.

If we consider the couple as ONE unit, there are 4! ways to arrange them around the circle x 2 ways the couple can sit. Hence the answer is:

5! - 2 * 4!
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 [#permalink] New post 02 Dec 2003, 17:07
how are there 5 ways to sit 6 people...shouldn't it be 6!......ahhh...i suck at math...
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 [#permalink] New post 02 Dec 2003, 17:30
5! ways to arrange 6 people = 120.

A person will be sitting adjacent to a certain person 40 percent of the time.

120 * .6 = 72
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 [#permalink] New post 03 Dec 2003, 10:41
For simplicity, let's call the two people who cannot sit together "Newt" and "Bill".

There are five different people who could be seated next to Newt. There are two seats adjacent to Newt, let's call them left and right.

There are three seats not adjacent to Newt.

Out of those five seats which Newt does not occupy, two of them, or 40%, are left or right, and cannot be occupied by Bill.

Make sense?
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 [#permalink] New post 03 Dec 2003, 10:43
If order matters, there are 6! arrangements, but you still throw out 40% of those cases.
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Please explain [#permalink] New post 03 Dec 2003, 13:00
Why do we use 5! to get the number of possibilities for 6 people in a circle?

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 [#permalink] New post 03 Dec 2003, 13:10
In circular arrangement, whatever may be the position the first person takes (either 1st or 2nd ..whatever) arrangement will not change.
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Explanation [#permalink] New post 03 Dec 2003, 14:41
I know I'm asking a lot, but could you guys explain this problem in such a way a baby could understand it? :) I'm having trouble understanding the 4! * 2 part of this answer.

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 [#permalink] New post 03 Dec 2003, 14:45
csperber-

AkamaiBrah and Praetorian have solved the problem in a slightly different way than I did. Do you understand either method?

PS- babies usually can't understand probability.

Last edited by stoolfi on 03 Dec 2003, 14:47, edited 1 time in total.
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I understand ... [#permalink] New post 03 Dec 2003, 14:46
the 5! to get the total number of possibilities ...

that's where I am! :)

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 [#permalink] New post 05 Dec 2003, 01:56
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 [#permalink] New post 05 Dec 2003, 01:59
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 [#permalink] New post 05 Dec 2003, 02:09
please, add these links to our link collection!
  [#permalink] 05 Dec 2003, 02:09
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