a tricky one

This topic has expert replies
Legendary Member
Posts: 512
Joined: Mon Jun 18, 2012 11:31 pm
Thanked: 42 times
Followed by:20 members

a tricky one

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
Work hard in Silence, Let Success make the noise.

If you found my Post really helpful, then don't forget to click the Thank/follow me button. :)
Source: — Problem Solving |

User avatar
Master | Next Rank: 500 Posts
Posts: 283
Joined: Sun Jun 23, 2013 11:56 pm
Location: Bangalore, India
Thanked: 97 times
Followed by:26 members
GMAT Score:750

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?

Cheers
Every job is a self-portrait of the person who did it. Autograph your work with excellence.

Kelley School of Business (Class of 2016)
GMAT Score: 750 V40 Q51 AWA 5 IR 8
https://www.beatthegmat.com/first-attemp ... tml#688494

User avatar
Senior | Next Rank: 100 Posts
Posts: 90
Joined: Wed Jun 26, 2013 10:55 pm
Thanked: 11 times
Followed by:1 members

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.

Cheers
The GMAT can be destroyed.

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3