more permutations...

Expert replies

Options: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Sun Jul 03, 2011 7:13 am; Thanked: 2 times

by Options » Sun Jul 03, 2011 8:35 am

sigh i'm stuck with this question some1 help!

Jane, Bryan, Sheryl, David and Ben went to a concert. Ben has a crush on Sheryl, while Bryan is not on speaking terms with David. How many arrangements are possible if
1) Ben insists on sitting next to Sheryl
2) Bryan refuses to sit next to David

Like this post

Source: Beat The GMAT — Problem Solving | Sun Jul 03, 2011 8:35 am

Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Sun Jul 03, 2011 8:47 am

Hi,
Let Ben and Sheryl be grouped together. So, we have 3 persons +1 group of Ben and Sheryl.
So, they can be arranged in 4! ways
group of Ben and Sheryl can be permuted in 2! ways
So, number of ways in 4!*2! = 48 ways
Now, these include Bryan and David together as well.
Let's consider the case of Bryan and David together as well. So we make them a group.
Number of ways is 3!*2!*2! = 24ways
So, for them not to be together, the number of ways is 48-24 = 24ways.

(OR)

Jane, Bryan, Sheryl, David and Ben went to a concert. Ben has a crush on Sheryl,
Consider __ Jane__(Ben+Sheryl)__
Jane and (Ben+Sheryl can be arranged in 2!*2! = 4 ways.
There are 3 gaps in which David and Bryan can be filled.
This can be done in 3P2 = 6 ways.
So, total number of ways is 4*6 = 24 ways

Cheers!

Things are not what they appear to be... nor are they otherwise

Like this post

amit2k9: Master | Next Rank: 500 Posts; Posts: 461; Joined: Tue May 10, 2011 9:09 amFollowed by: 3 members; Location: pune; Thanked: 36 times

by amit2k9 » Sun Jul 03, 2011 11:18 pm

questions like there you should use symmetry.

Ben and Sheryl sit together.

total people 4 (Be-Sh one group)
also Be-SH can sit in 2! ways

thus total ways = 2!*4! = 48.
in half if these 48 cases D and Br will sit apart and in half they will sit together.

thus total cases = 48/2 = 24.

For Understanding Sustainability,Green Businesses and Social Entrepreneurship visit -https://aamthoughts.blocked/
(Featured Best Green Site Worldwide-https://bloggers.com/green/popular/page2)

Like this post

sunilrawat: Master | Next Rank: 500 Posts; Posts: 112; Joined: Sun Jun 13, 2010 9:20 am; Thanked: 5 times; GMAT Score:640

by sunilrawat » Mon Jul 04, 2011 1:12 am

amit2k9 wrote: in half if these 48 cases D and Br will sit apart and in half they will sit together.

thus total cases = 48/2 = 24.

why half the cases? please explain

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 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