NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 09:16 It is currently 26 Apr 2024, 09:16
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

A librarian has a set of ten books, including four different books abo

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
G
mikemcgarry
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4452
Own Kudos [?]: 28574 [12]
Given Kudos: 130
A librarian has a set of ten books, including four different books abo [#permalink] New post   20 Jan 2015, 11:46
2
Kudos
10
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

25% (medium)

Question Stats:

70% (01:10) correct 30% (01:16) wrong based on 326 sessions
Hide Show timer Statistics
A librarian has a set of ten books, including four different books about Abraham Lincoln. The librarian wants to put the ten books on a shelf with the four Lincoln books next to each other, somewhere on the shelf among the other six books. How many different arrangements of the ten books are possible?
(A) (10!)/(4!)
(B) (4!)(6!)
(C) (4!)(7!)
(D) (4!)(10!)
(E) (4!)(6!)(10!)

For a set of Counting Practice Problems for the GMAT, as well as the OE for this particular question, see:
https://magoosh.com/gmat/2015/counting-p ... -the-gmat/

Mike :-)
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
aviram
Manager
Manager
Joined: 27 Jun 2014
Posts: 60
Own Kudos [?]: 113 [5]
Given Kudos: 125
Location: New Zealand
Concentration: Strategy, General Management
GMAT 1: 710 Q43 V45
GRE 1: Q161 V163

GRE 2: Q159 V166
GPA: 3.6
WE:Editorial and Writing (Computer Software)
Send PM
Re: A librarian has a set of ten books, including four different books abo [#permalink] New post   20 Jan 2015, 15:29
4
Kudos
1
Bookmarks
mikemcgarry wrote:
A librarian has a set of ten books, including four different books about Abraham Lincoln. The librarian wants to put the ten books on a shelf with the four Lincoln books next to each other, somewhere on the shelf among the other six books. How many different arrangements of the ten books are possible?
(A) (10!)/(4!)
(B) (4!)(6!)
(C) (4!)(7!)
(D) (4!)(10!)
(E) (4!)(6!)(10!)

For a set of Counting Practice Problems for the GMAT, as well as the OE for this particular question, see:
https://magoosh.com/gmat/2015/counting-p ... -the-gmat/

Mike :-)


Hi Mike,

You can club the four Lincoln books as one, which leaves us with six other books plus this one to think about. So, these seven items can be arranged in 7! ways, and since the four books can be moved around among themselves with each combination giving us a new overall combination, we have an additional 4! ways. Therefore, the answer would be 7!*4!, which is C.
General Discussion
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6818
Own Kudos [?]: 29939 [4]
Given Kudos: 799
Location: Canada
Send PM
Re: A librarian has a set of ten books, including four different books abo [#permalink] New post   24 Aug 2018, 07:23
4
Kudos
Expert Reply
Top Contributor
mikemcgarry wrote:
A librarian has a set of ten books, including four different books about Abraham Lincoln. The librarian wants to put the ten books on a shelf with the four Lincoln books next to each other, somewhere on the shelf among the other six books. How many different arrangements of the ten books are possible?
(A) (10!)/(4!)
(B) (4!)(6!)
(C) (4!)(7!)
(D) (4!)(10!)
(E) (4!)(6!)(10!)

For a set of Counting Practice Problems for the GMAT, as well as the OE for this particular question, see:
https://magoosh.com/gmat/2015/counting-p ... -the-gmat/

Mike :-)


Let's first "glue" the 4 Lincoln books together to create one SUPER BOOK (this will ensure that the 4 books remain together)
We now have 7 books: 6 regular books and 1 super book
We can arrange these 7 books in 7! ways.

KEY: For each of the 7! arrangements, we can take the 4 Lincoln books (that comprise the SUPER BOOK) and arrange them in 4! ways.
So, the TOTAL number of arrangements = (7!)(4!)

Answer: C

Cheers,
Brent
User avatar
S
Gmatprep550
Manager
Manager
Joined: 21 Jul 2018
Posts: 149
Own Kudos [?]: 65 [0]
Given Kudos: 186
Send PM
Reviews Badge
Re: A librarian has a set of ten books, including four different books abo [#permalink] New post   23 Dec 2018, 17:51
Hi,

I am not getting one thing in both the answer, question states they have 4 different book of AB Li then how you can count them as one?

GMATPrepNow aviram mikemcgarry
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6818
Own Kudos [?]: 29939 [2]
Given Kudos: 799
Location: Canada
Send PM
Re: A librarian has a set of ten books, including four different books abo [#permalink] New post   11 Jan 2019, 08:25
2
Kudos
Expert Reply
Top Contributor
Gmatprep550 wrote:
Hi,

I am not getting one thing in both the answer, question states they have 4 different book of AB Li then how you can count them as one?

GMATPrepNow aviram mikemcgarry


We are treating the 4 Abraham Lincoln as different.
There are 4! ways (24 ways) to arrange these 4 books in a row.
Once we arrange these 4 different books in a row, we "glue" them together so that we can ensure that they stay together. Those 4 books are still different books, they are just glued together.
Does that help?

Cheers,
Brent
User avatar
G
gmexamtaker1
Manager
Manager
Joined: 16 Jul 2018
Posts: 213
Own Kudos [?]: 68 [1]
Given Kudos: 261
Send PM
GMAT ToolKit User Reviews Badge
Re: A librarian has a set of ten books, including four different books abo [#permalink] New post   11 Jan 2019, 08:50
1
Kudos
Gmatprep550 wrote:
Hi,

I am not getting one thing in both the answer, question states they have 4 different book of AB Li then how you can count them as one?

GMATPrepNow aviram mikemcgarry


Hey Gmatprep550 ,

Well it is a way to make your life easier , you consider those 4 books as an single entity so that you can address the problem in an easier way ,remember that they have to be next to each other.
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18761
Own Kudos [?]: 22056 [0]
Given Kudos: 283
Location: United States (CA)
Send PM
Re: A librarian has a set of ten books, including four different books abo [#permalink] New post   21 Jan 2019, 18:45
Expert Reply
mikemcgarry wrote:
A librarian has a set of ten books, including four different books about Abraham Lincoln. The librarian wants to put the ten books on a shelf with the four Lincoln books next to each other, somewhere on the shelf among the other six books. How many different arrangements of the ten books are possible?
(A) (10!)/(4!)
(B) (4!)(6!)
(C) (4!)(7!)
(D) (4!)(10!)
(E) (4!)(6!)(10!)


Since the 4 Lincoln books must be together, we can, for now, treat them as just 1 book. Since there are 6 other books, there are a total of 1 + 6 = 7 books, and hence there are 7! arrangements. However, within these 4 Lincoln books, there are 4! ways to arrange them. Therefore, the total number of arrangements of all 10 books, with the 4 Lincoln books together, is:

4! * 7!

Answer: C
User avatar
B
gmatpro15
Manager
Manager
Joined: 09 Aug 2022
Posts: 86
Own Kudos [?]: 22 [0]
Given Kudos: 48
Location: India
Concentration: General Management, Leadership
GPA: 4
WE:Design (Real Estate)
Send PM
Re: A librarian has a set of ten books, including four different books abo [#permalink] New post   22 Aug 2022, 22:51
Since the 4 Lincoln books must be together, we can, for now, treat them as just 1 book. Since there are 6 other books, there are a total of 1 + 6 = 7 books, and hence there are 7! arrangements. However, within these 4 Lincoln books, there are 4! ways to arrange them. Therefore, the total number of arrangements of all 10 books, with the 4 Lincoln books together, is:

4! * 7!
GMAT Club Bot
gmatclubot
Re: A librarian has a set of ten books, including four different books abo [#permalink]
22 Aug 2022, 22:51
Moderators:
Bunuel
Math Expert
92945 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions