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

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CEO
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In how many ways can 6 ppl be seated in a circle if 2 ppl [#permalink]  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?
Intern
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Re: PS : Probability ( Circular arrangement) [#permalink]  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)

Amar.
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Re: PS : Probability ( Circular arrangement) [#permalink]  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

Thanks
Praetorian
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Re: PS : Probability ( Circular arrangement) [#permalink]  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.

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

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

thanks
praetorian
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Re: PS : Probability ( Circular arrangement) [#permalink]  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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AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

Manager
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how are there 5 ways to sit 6 people...shouldn't it be 6!......ahhh...i suck at math...
Director
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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
Director
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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?
Director
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If order matters, there are 6! arrangements, but you still throw out 40% of those cases.
Manager
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Why do we use 5! to get the number of possibilities for 6 people in a circle?

Thanks,
CJ
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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]  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.

Thanks,
CJ
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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]  03 Dec 2003, 14:46
the 5! to get the total number of possibilities ...

that's where I am!

CJ
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