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a tricky one

Expert replies
by sana.noor » Mon Aug 19, 2013 7:55 pm
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 the probability that any two of them directly face each other?

A) 1/56

B) 1/8

C) 1/7

D) 15/56

E) 4/7

OA is C

suppose their are 8 people A,B,C,D,E,F,G,H....so question is asking that what is the probability that A and B directly facing each other. if A selected a seat then B can select 1 seat from 7 options. so the right answer is [spoiler]1/7[/spoiler] however, i google this question and found that most of the explanation says its 4/7
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Source: — Problem Solving |

by ganeshrkamath » Mon Aug 19, 2013 8:23 pm
sana.noor wrote: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 the probability that any two of them directly face each other?

A) 1/56

B) 1/8

C) 1/7

D) 15/56

E) 4/7

OA is C

suppose their are 8 people A,B,C,D,E,F,G,H....so question is asking that what is the probability that A and B directly facing each other. if A selected a seat then B can select 1 seat from 7 options. so the right answer is [spoiler]1/7[/spoiler] however, i google this question and found that most of the explanation says its 4/7
Suppose we need to find the probability of 2 people A and B facing each other.
Now A can be in any of the 8 seats and B should be in the opposite seat.
So there will be three seats on each side for others.
So favourable cases = 8*6C3*3!*3! = 8*6!

All cases (sample space) = 8C4 * 4! * 4! = 8!

Required probability = (8*6!)/(8!)
[spoiler]= 1/7[/spoiler]

The OA is right.

Can you post the explanation for 4/7 here?

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by macattack » Tue Aug 20, 2013 4:28 am
That how I would tackle it:
Total number of outcomes: 8C2= 28 (Number of ways two people can be seated in 8 seats)
Desired outcomes: 4 (Number of ways two people can be facing each other when seated on a rectangular table with four seats on each side)

Probability=4/28=1/7

The OA is right Google isn't.

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by GMATGuruNY » Tue Aug 20, 2013 6:29 am
sana.noor wrote: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 the probability that any two of them directly face each other?

A) 1/56

B) 1/8

C) 1/7

D) 15/56

E) 4/7
Each of the 8 people is to be seated at the table.
Question rephrased: Once A has been seated, what is the probability that B sits directly opposite A?
Since B must choose 1 of the 7 remaining seats, the probability that B selects the seat directly opposite A = 1/7.

The correct answer is C.
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