Probability...a cracker

Expert replies

fightthegmat: Senior | Next Rank: 100 Posts; Posts: 31; Joined: Wed Jan 14, 2009 11:45 am; Thanked: 1 times; GMAT Score:600

by fightthegmat » Mon Sep 07, 2009 12:18 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

how do you work on this? the tough part is 'couples to be seated NOT adjacent to each other'.

Like this post

Source: Beat The GMAT — Problem Solving | Mon Sep 07, 2009 12:18 am

Nermal: Senior | Next Rank: 100 Posts; Posts: 77; Joined: Sun Jun 21, 2009 10:25 am; Location: Germany; Thanked: 7 times

by Nermal » Mon Sep 07, 2009 10:00 am

IMO B (1/4)

probability is the number of desired outcomes divided by the number of possible outcomes.

no. of possible outcomes: 5!=120
no. of desired outcomes: 5!/(2!*2!)=30
(I drew a line for each person and labelled the persons C1,C1,C2,C2,S)
30/120=1/4

Like this post

rish: Senior | Next Rank: 100 Posts; Posts: 65; Joined: Fri Jul 24, 2009 11:47 am; Thanked: 5 times

by rish » Mon Sep 07, 2009 10:09 am

IMO D

Probability for NO couple to sit together = 1 - (Probability of at least 1 couple sitting together)

Ways in which the first couple can sit together = 2*4! (1 couple is considered one unit,the couple sitting together can be arranged in 2 ways)
Ways for second couple = 2*4!

These cases include an extra case of both couples sitting together
Ways in which both couple are seated together = 2*2*3! = 4! (2 couples considered as 2 units- so each couple can be arrange between themselves in 2 ways and the 3 units in 3! Ways)

Thus total ways in which at least one couple is seated together = 2*4! + 2*4! - 4! = 3*4!

Total ways to arrange the 5 ppl = 5!
Thus, prob of at least one couple seated together = 3*4! / 5! = 3/5

Thus prob of none seated together = 1 - 3/5 = 2/5

Like this post

fightthegmat: Senior | Next Rank: 100 Posts; Posts: 31; Joined: Wed Jan 14, 2009 11:45 am; Thanked: 1 times; GMAT Score:600

by fightthegmat » Mon Sep 07, 2009 10:19 am

Nermal wrote:IMO B (1/4)

probability is the number of desired outcomes divided by the number of possible outcomes.

no. of possible outcomes: 5!=120
no. of desired outcomes: 5!/(2!*2!)=30
(I drew a line for each person and labelled the persons C1,C1,C2,C2,S)
30/120=1/4

The answer is D

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