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GRE Math Challenge #13 - Six people are asked to sit down in

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GRE Math Challenge #13 - Six people are asked to sit down in [#permalink] New post 19 Sep 2014, 02:39
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Six people are asked to sit down in a circle consisting of eight chairs.Assume that the six people are in fact three couples.What is the probability that at least one of the three wives will sit next to her husband if everybody takes a seat randomly.

[Reveal] Spoiler: Answer
P = 6/7
Number of arrangements where at least one wife sits next to her husband:

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Re: GRE Math Challenge #13 [#permalink] New post 25 Sep 2014, 12:33
pls explain me ............
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Re: GRE Math Challenge #13 [#permalink] New post 26 Sep 2014, 01:38
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The question states at least one partner sits next to other in the circular arrangement. Now Initially we had to arrange 8 objects in a circular formation. 6 persons(distinguishable) and two vacant spaces (non distinguishable). So number of arrangements would be 8!/8*2! = 2520.

Now lets assume we have a couple now the problem becomes 4 persons + 1 couple + 2 blank spaces in 7 chairs. So number of arrangements 7!/ 7 * 2! = 2160.

Divide to obtain probability: 6/7.
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Re: GRE Math Challenge #13 [#permalink] New post 02 Jul 2017, 10:54
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sandy wrote:
The question states at least one partner sits next to other in the circular arrangement. Now Initially we had to arrange 8 objects in a circular formation. 6 persons(distinguishable) and two vacant spaces (non distinguishable). So number of arrangements would be 8!/8*2! = 2520.

Now lets assume we have a couple now the problem becomes 4 persons + 1 couple + 2 blank spaces in 7 chairs. So number of arrangements 7!/ 7 * 2! = 2160.

Divide to obtain probability: 6/7.


won't the two people who form the couple arrange among themselves in 2 ways?
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Re: GRE Math Challenge #13 - Six people are asked to sit down in [#permalink] New post 03 Jul 2017, 01:26
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Re: GRE Math Challenge #13 - Six people are asked to sit down in [#permalink] New post 04 Jul 2017, 08:53
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sandy wrote:
Six people are asked to sit down in a circle consisting of eight chairs.Assume that the six people are in fact three couples.What is the probability that at least one of the three wives will sit next to her husband if everybody takes a seat randomly.

[Reveal] Spoiler: Answer
P = 6/7
Number of arrangements where at least one wife sits next to her husband:


Using complement rule
That is, P(Event A happening) = 1 - P(Event A not happening)

So, here we get: P(at least 1 matching couple) = 1 - P(zero matching couple)


P(zero matching couple) =6/8 x 4/7 x 2/6
= 1/7

So, P(at least 1 couple) = 1 - P(no couple)
= 1 - 1/7
= 6/7
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Re: GRE Math Challenge #13 - Six people are asked to sit down in   [#permalink] 04 Jul 2017, 08:53
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