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Two couples and one single person are seated at random in a

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Two couples and one single person are seated at random in a [#permalink] New post 22 May 2005, 12:06
Two couples and one single person are seated at random in a row of 5 chairs. What is the probability that neither of the couples sits together in adjacent chairs?
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 [#permalink] New post 22 May 2005, 12:19
Let me know if 13/24 is correct. I would explain then
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 [#permalink] New post 22 May 2005, 12:24
Nope, the OA is 2/5. And frankly, I cannot understand their explanation. Its a 25 line explanation. :(
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 [#permalink] New post 22 May 2005, 12:27
This was discussed before...Heres the link

http://www.gmatclub.com/phpbb/viewtopic ... 9976#89976
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 [#permalink] New post 22 May 2005, 20:51
Can some one let me know the gap in this process?

Total outcomes = 5! =120

Lets says that we have the 2 couple as 2 blocks occupying 4 seats.

SO we have 2 blocks( each block has a couple) and 1 individual.

So they can be arranges in 3!.2!.2! (Since the couples can shuffle between themselves)

So if they sit together it would be 24/120 = 1/5 and probablity of not sitting together is 4/5....


Whats the flaw in this logic? Please explain
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 [#permalink] New post 22 May 2005, 21:08
What if one of the couples sits together and the other doesn't?
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 [#permalink] New post 22 May 2005, 21:08
gmat2me2 wrote:
Can some one let me know the gap in this process?

Total outcomes = 5! =120

Lets says that we have the 2 couple as 2 blocks occupying 4 seats.

SO we have 2 blocks( each block has a couple) and 1 individual.

So they can be arranges in 3!.2!.2! (Since the couples can shuffle between themselves)

So if they sit together it would be 24/120 = 1/5 and probablity of not sitting together is 4/5....


Whats the flaw in this logic? Please explain


What if one couple sits together and one doesn't?
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 [#permalink] New post 22 May 2005, 21:10
:lol: Great minds think alike don't they? :-D
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 [#permalink] New post 22 May 2005, 21:10
Just to clarify, HongHu and I aren't the same person. Just happened to post at the same time :)
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 [#permalink] New post 22 May 2005, 21:13
HongHu wrote:
What if one of the couples sits together and the other doesn't?



But we were asked in the question how many ways the 2 couples cannot sit together....So I subtracted 1 - (Probablity of 2 couples sitting together)....

So you mean to say that 1 couple sit together but the other aint...Isnt it ?

So that could be 4!*2 ...Is this correct?
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 [#permalink] New post 22 May 2005, 21:15
sparky wrote:
Just to clarify, HongHu and I aren't the same person. Just happened to post at the same time :)


Boy you guys scared me enough Its 12:15 AM here I am going to bed :-)
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 [#permalink] New post 23 May 2005, 20:47
gmat2me2 wrote:
HongHu wrote:
What if one of the couples sits together and the other doesn't?



But we were asked in the question how many ways the 2 couples cannot sit together....So I subtracted 1 - (Probablity of 2 couples sitting together)....

So you mean to say that 1 couple sit together but the other aint...Isnt it ?

So that could be 4!*2 ...Is this correct?


So the each of the 2 couples can sit together in 4!*2! ways = 48 ways

Since there are 2 couple = 96 ways.

But this included both the couples sitting toghether = 3!*2!*2! = 24 (I was confused at this point but now I think I understand the question)

96-24 = 72 ways only one couple can sit togther

probability of Neither of couple sitting together is= 72/120 = 3/5
  [#permalink] 23 May 2005, 20:47
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