Last visit was: 24 Jul 2024, 10:56 It is currently 24 Jul 2024, 10:56
Toolkit
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

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.

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

SORT BY:
Tags:
Show Tags
Hide Tags
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4490
Own Kudos [?]: 28869 [12]
Given Kudos: 130
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)
General Discussion
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30861 [4]
Given Kudos: 799
Manager
Joined: 21 Jul 2018
Posts: 148
Own Kudos [?]: 65 [0]
Given Kudos: 186
Re: A librarian has a set of ten books, including four different books abo [#permalink]
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
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30861 [2]
Given Kudos: 799
Re: A librarian has a set of ten books, including four different books abo [#permalink]
2
Kudos
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
Manager
Joined: 16 Jul 2018
Posts: 213
Own Kudos [?]: 68 [1]
Given Kudos: 261
Re: A librarian has a set of ten books, including four different books abo [#permalink]
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.
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19190
Own Kudos [?]: 22715 [0]
Given Kudos: 286
Location: United States (CA)
Re: A librarian has a set of ten books, including four different books abo [#permalink]
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!

Manager
Joined: 09 Aug 2022
Posts: 85
Own Kudos [?]: 23 [0]
Given Kudos: 48
Location: India
Concentration: General Management, Leadership
GPA: 4
WE:Design (Real Estate)
Re: A librarian has a set of ten books, including four different books abo [#permalink]
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!
Re: A librarian has a set of ten books, including four different books abo [#permalink]
Moderator:
Math Expert
94606 posts