A rectangular table seats 4 people on each of two sides, : PS Archive
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# A rectangular table seats 4 people on each of two sides,

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Manager
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A rectangular table seats 4 people on each of two sides, [#permalink]

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11 Aug 2005, 13:05
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A rectangular table seats 4 people on each of two sides, with every person directly facing another person across the table. If eight people choose their seats at random, what is probability that any two of them directly face other?

(A) 1/56

(B) 1/8

(C) 1/7

(D) 15/56

(E) 4/7

Will post the OA in couple of days.
SVP
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11 Aug 2005, 13:41
Hmmm my reading to this is that say person S and T belong the 8 people then what is the probability of them directly facing each other? If this is the case then no matter where S sits there's only 7 seats left for T so the probability of T directly facing S would be 1/7.
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Senior Manager
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11 Aug 2005, 18:40
since one can only another person from across the table
(with every person directly facing another person across the table),
shouldn't this be 4/7 then ?
Senior Manager
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13 Aug 2005, 08:12
This a tricky exercises
can we have the OA and the OE
thanks
Manager
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13 Aug 2005, 08:33
I think honghu is right with 1/7 for the reason she gives.
Senior Manager
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13 Aug 2005, 17:11
yes 1/7 should be the answer

pick 1 from the rest of 7 and have him sitting on the opposite side, the probablity is: 4/7; after that, pick 1 of the 4 position across from you is 1/4,
therefore (4/7)*(1/4) = 1/7
Manager
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14 Aug 2005, 00:42
The OA is 1/7 = choice C.

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