Last visit was: 11 Jul 2025, 04:35 It is currently 11 Jul 2025, 04:35
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
User avatar
282552
Joined: 19 Mar 2012
Last visit: 02 Nov 2018
Posts: 80
Own Kudos:
300
 [38]
Given Kudos: 368
Location: United States
Schools: IIMA PGPX"20
Schools: IIMA PGPX"20
Posts: 80
Kudos: 300
 [38]
2
Kudos
Add Kudos
36
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 10 Jul 2025
Posts: 102,634
Own Kudos:
Given Kudos: 98,170
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,634
Kudos: 740,332
 [13]
7
Kudos
Add Kudos
6
Bookmarks
Bookmark this Post
User avatar
vitaliyGMAT
Joined: 13 Oct 2016
Last visit: 26 Jul 2017
Posts: 297
Own Kudos:
843
 [5]
Given Kudos: 40
GPA: 3.98
Posts: 297
Kudos: 843
 [5]
3
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
General Discussion
User avatar
hanyhamdani
User avatar
Current Student
Joined: 30 Dec 2013
Last visit: 04 Jan 2019
Posts: 28
Own Kudos:
28
 [1]
Given Kudos: 26
Status:preparing
Location: United Arab Emirates
Concentration: Technology, Entrepreneurship
GMAT 1: 660 Q45 V35
GMAT 2: 640 Q49 V28
GPA: 2.84
WE:General Management (Consumer Packaged Goods)
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
282552
A child received a gift of six different soccer team flags, including Liverpool and Arsenal. If he only has space in his bedroom to display four flags in a row, how many arrangements are possible if he cannot display the Liverpool and Arsenal flags at the same time?

A) 162
B) 216
C) 272
D) 360
E) 414

Firstly,
Total number of ways to select 4 flags out of 6 are: T= 6p4 = 360 ways
Now we have to deduct the ways in which Liverpool and Arsenal flags could possibly be placed together.
Lets select flags which include both arsenal and liverpool
L A _ _
these 4 flags can be arranged in 4x3x2x1 =24 ways
which 2 flags to select among 4 flags ( total - L-A=4) = 4C2=6
SO total number of arrangements in which L & A are there at same time = 24x6=144

so, 360-144 = 216 arrangements
B

Kudos please 8-) 8-)
User avatar
JeffTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 04 Mar 2011
Last visit: 05 Jan 2024
Posts: 2,996
Own Kudos:
7,922
 [4]
Given Kudos: 1,646
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Expert
Expert reply
Posts: 2,996
Kudos: 7,922
 [4]
4
Kudos
Add Kudos
Bookmarks
Bookmark this Post
282552
A child received a gift of six different soccer team flags, including Liverpool and Arsenal. If he only has space in his bedroom to display four flags in a row, how many arrangements are possible if he cannot display the Liverpool and Arsenal flags at the same time?

A) 162
B) 216
C) 272
D) 360
E) 414

We are given that a child received 6 different soccer team flags, including Liverpool and Arsenal. We need to determine the number of arrangements that are possible when the flags are displayed 4 at a time and the Arsenal and Liverpool flags are not displayed at the same time.

To start we can create the following equation:

Total number of ways to display the flags = (number of ways to display the flags when both the Arsenal and Liverpool flags are displayed together) + (number of ways to display the flags when the Arsenal and Liverpool flags are not displayed together).

Let’s first determine the total number of ways to display the 4 flags from a choice of 6 flags.

This is a permutation problem because the order in which the flags are displayed is important.

Number of ways to display the 4 flags from 6 flags = 6P4 = 6 x 5 x 4 x 3 = 360

Next we can determine the number of ways to display the flags when both Arsenal and Liverpool are displayed. Since we know that the Arsenal and Liverpool flags are definitely selected, that leaves us with 4 flags for the 2 remaining spots, so there are 4C2 ways to select the two remaining flags, which equals (4 x 3)/2! = 6 ways. Finally, there are 4! ways to arrange those 4 flags, which equals 24 ways. Thus, there are 24 x 6 = 144 ways to select and arrange the flags in which both Arsenal and Liverpool are displayed.

Finally, there are 360 - 144 = 216 ways to select and arrange the 4 flags when Arsenal and Liverpool cannot be displayed at the same time.

Answer: B
User avatar
Cez005
Joined: 13 Dec 2013
Last visit: 11 Feb 2020
Posts: 96
Own Kudos:
Given Kudos: 122
Location: United States (NY)
Concentration: General Management, International Business
GMAT 1: 710 Q46 V41
GMAT 2: 720 Q48 V40
GPA: 4
WE:Consulting (Consulting)
Products:
GMAT 2: 720 Q48 V40
Posts: 96
Kudos: 143
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Total number of ways to arrange four flags from 6 = 4P6 = 6*5*4*3 = 360

Number of ways with Arsenal AND Liverpool flags: Set Arsenal and Liverpool in the first two spaces and determine the possible arrangements for the remaining two spaces (out of four). 2C4 = (4*3)/2=6. So there are 6 combinations that include Liverpool and Arsenal. Each of these 6 combinations can be ordered in 4! ways. So number of ways with Arsenal AND Liverpool = 6*4! = 144.

Number of desired arrangements = 360 - 144 = 216
User avatar
BillyZ
User avatar
Current Student
Joined: 14 Nov 2016
Last visit: 03 May 2025
Posts: 1,147
Own Kudos:
21,910
 [1]
Given Kudos: 926
Location: Malaysia
Concentration: General Management, Strategy
GMAT 1: 750 Q51 V40 (Online)
GPA: 3.53
Products:
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
282552
A child received a gift of six different soccer team flags, including Liverpool and Arsenal. If he only has space in his bedroom to display four flags in a row, how many arrangements are possible if he cannot display the Liverpool and Arsenal flags at the same time?

A) 162
B) 216
C) 272
D) 360
E) 414

OFFICIAL SOLUTION



A helpful way to begin this problem is to consider how many options the boy would have were there no restriction. With 6 flags to choose from and 4 spaces for them, he would then have 6 choices for the first flag, 5 for the second, 4 for the third, and 3 for the fourth, for a total of \(6 * 5 * 4 * 3 = 360\) options. But there is a restriction, so you know that there are fewer options than 360. This at the very least allows you to eliminate choices D and E while you investigate the restriction.

Now you want to determine how many arrangements would violate the restriction. For those arrangements, Liverpool and Arsenal are definitely displayed together. That means that of the 4 other flags, you will need to select 2 to make the group (that's a combination), and then you will have 4 flags to arrange (that's how you'll bring it back to a permutation). selecting 2 out of 4 means that you'll use \(\frac{4!}{{2!2!}}\), which becomes \(\frac{4∗3}{2}=6\) combinations for which the two flags will appear together. Then multiply that by the number of ways to arrange each group of 4, which is 4!. That means that 144 of the 360 arrangements will not work, so that leaves 216 possible arrangements, which is answer choice B.
User avatar
chesstitans
Joined: 12 Dec 2016
Last visit: 20 Nov 2019
Posts: 990
Own Kudos:
Given Kudos: 2,562
Location: United States
GMAT 1: 700 Q49 V33
GPA: 3.64
GMAT 1: 700 Q49 V33
Posts: 990
Kudos: 1,898
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I really like if the math problems of arrangement or possibilities only concerns with a small number of factors in each group and with a small number of groups.
this question is such an example.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,374
Own Kudos:
Posts: 37,374
Kudos: 1,010
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderators:
Math Expert
102634 posts
PS Forum Moderator
686 posts