In how many ways can 6 ppl be seated in a circle if 2 ppl : PS Archive
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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]

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01 Oct 2003, 13:22
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In how many ways can 6 ppl be seated in a circle if 2 ppl are always separated.

Two girls have their birthdays in the same week.It is known that one
of the girls was born on a saturday. determine the prob that both
were born on a saturday.
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Joined: 29 Aug 2003
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Location: Detroit, MI
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Re: PS : Counting Methods and Probability [#permalink]

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02 Oct 2003, 06:06
praetorian123 wrote:
In how many ways can 6 ppl be seated in a circle if 2 ppl are always separated.

Two girls have their birthdays in the same week.It is known that one
of the girls was born on a saturday. determine the prob that both
were born on a saturday.

Let me try ....

The total number of ways in which N people can be seated in a circle = (N - 1)!

If two people (say A and B) are next to each other, the remaining (N-2) people can be arranged in (N-2)! ways - in one direction and (N-2)! more ways in the other direction i.e. 2*(N-2)! ways

So, answer = (N - 1)! - 2*(N-2)! = 5! - 2*4! = 120 - 48 = 72

I think this can be generalized to say that of N people, 2*(N-t)! ways exist in which t of N are next to one another, where t < N and (N-1)! - 2*(N-t)! ways exist in which t of N people are not next to one another.

Am I right?

Is the answer 1/7 for the second one?

Given that the two girls were born in the same week, the probability will be 1 of the seven days.
Re: PS : Counting Methods and Probability   [#permalink] 02 Oct 2003, 06:06
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