Princeton -Probability

Expert replies

tutonaranjo: Senior | Next Rank: 100 Posts; Posts: 42; Joined: Wed Jun 20, 2007 8:45 am; Thanked: 1 times

by tutonaranjo » Thu Sep 20, 2007 11:58 am

Two couples and one single person are seated at random in a row of five chairs. What is the probability that neither of the couples sits together in adjacent chairs?
a) 1/5
b) 1/4
c) 3/8
d) 2/5
e) 1/2

Answer is D. Someone help with detailed explanation?

Like this post

Source: Beat The GMAT — Problem Solving | Thu Sep 20, 2007 11:58 am

kajcha: Master | Next Rank: 500 Posts; Posts: 321; Joined: Tue Aug 28, 2007 5:42 am; Thanked: 1 times

by kajcha » Thu Sep 20, 2007 1:04 pm

Total no of ways 5 people can sit = 5! = 120

Assume one couple as 1 entity. So, there are only 4 entities. This combination can sit in 4! ways.
2 person in the couple can sit in 2! ways.

So, total no of ways = 2!*4! = 48 ---------- (1)

Similarly for another set of couple, total no of ways = 48 ---------- (2)

Total no of ways both couple will sit together = 2*2*3! = 24 --------(3)

In (1) and (2) we have calculated (3) already. So we need to subtract it once from the total otherwise it will be counted twice.

So total no of ways (at least one couple sit together) = 48+48-24 = 72

So probability of at least one couple sitting together = 72/120

Probability (neither couple sits together) = 1-72/120 = 2/5

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review