• NEW! FREE Beat The GMAT Quizzes
Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## A librarian has a set of ten books, including four different ##### This topic has 2 expert replies and 2 member replies ### Top Member ## A librarian has a set of ten books, including four different ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult 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!) OA C Source: Magoosh ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1114 messages Followed by: 29 members Upvotes: 59 Quote: A librarian has a set of ten different books, including four 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!) Source: Magoosh $$?\,\,\,:\,\,\,\# \,\,\,{\rm{possibilities}}\,{\rm{,}}\,\,{\rm{Abe}}\,\,{\rm{books}}\;\,{\rm{together}}$$ $$10\,\,{\rm{different}}\,\,{\rm{books,}}\,\,{\rm{4}}\,\,{\rm{about}}\,{\rm{Abe}}\,\,\,\, \Rightarrow \,\,\,\,\left\{ \matrix{ \,1\,\,{\rm{multiple - block}}\,\,\,\left( {4\,\,{\rm{Abe}}\,\,{\rm{books}}} \right) \hfill \cr \,6\,\,{\rm{single}}\,{\rm{blocks}} \hfill \cr} \right.$$ $$\left. \matrix{ {P_7} = 7!\,\,\,{\rm{permutation}}\,\,{\rm{of}}\,\,{\rm{all}}\,\,{\rm{blocks}} \hfill \cr {{\rm{P}}_{\rm{4}}} = 4!\,\,\,{\rm{permutation}}\,\,{\rm{of}}\,\,{\rm{Abe}}\,\,{\rm{books}}\,\,\,\, \hfill \cr} \right\}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,?\,\,\, = \,\,{P_7} \cdot {P_4}\,\, = \,\,7!4!\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {\rm{C}} \right)$$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br Master | Next Rank: 500 Posts Joined 15 Oct 2009 Posted: 321 messages Upvotes: 27 BTGmoderatorDC 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!) OA C Source: Magoosh Consider the 4 Lincoln books as one book for the purposes of arranging on the shelf, since they have to be together. Along with the 6 other books, you can see that there are then 7 positions occupied. With the idea that order matters, there are then 7! ways to arrange the books on the shelf. Going back to the 4 Lincoln books, since the problem stated that they are "different", we are being told that order matters, so the number of ways to arrange the 4 LIncoln books is 4!. Total ways to arrange the books is therefore C, 7!x4! ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12540 messages Followed by: 1245 members Upvotes: 5254 GMAT Score: 770 BTGmoderatorDC 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!) Take the task of arranging the 10 books and break it into stages. Stage 1: Arrange the 4 books about Abe Lincoln in a row We can arrange n objects in n! ways. So, we can arrange the 4 books in 4! ways IMPORTANT: Now we'll "glue" the 4 Abe Lincoln books together to form 1 SUPER BOOK (this will ensure that the 4 Abe Lincoln books remain together) So, we now have 1 Abe Lincoln SUPER BOOK, along with 6 non-Abe Lincoln books (for a total of 7 "books") Stage 2: Arrange the 7 "books" We can arrange n objects in n! ways. So, we can arrange the 7 books in 7! ways By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus arrange all of the books) in [color=blue](4!)(7!) ways Answer: C -------------------------- Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch our free video: http://www.gmatprepnow.com/module/gmat-counting/video/775 You can also watch a demonstration of the FCP in action: https://www.gmatprepnow.com/module/gmat-counting/video/776 Then you can try solving the following questions: EASY - http://www.beatthegmat.com/what-should-be-the-answer-t267256.html - http://www.beatthegmat.com/counting-problem-company-recruitment-t244302.html - http://www.beatthegmat.com/picking-a-5-digit-code-with-an-odd-middle-digit-t273110.html - http://www.beatthegmat.com/permutation-combination-simple-one-t257412.html - http://www.beatthegmat.com/simple-one-t270061.html MEDIUM - http://www.beatthegmat.com/combinatorics-solution-explanation-t273194.html - http://www.beatthegmat.com/arabian-horses-good-one-t150703.html - http://www.beatthegmat.com/sub-sets-probability-t273337.html - http://www.beatthegmat.com/combinatorics-problem-t273180.html - http://www.beatthegmat.com/digits-numbers-t270127.html - http://www.beatthegmat.com/doubt-on-separator-method-t271047.html - http://www.beatthegmat.com/combinatorics-problem-t267079.html DIFFICULT - http://www.beatthegmat.com/wonderful-p-c-ques-t271001.html - http://www.beatthegmat.com/permutation-and-combination-t273915.html - http://www.beatthegmat.com/permutation-t122873.html - http://www.beatthegmat.com/no-two-ladies-sit-together-t275661.html - http://www.beatthegmat.com/combinations-t123249.html Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### Top Member Legendary Member Joined 29 Oct 2017 Posted: 732 messages Followed by: 4 members 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!) Hence, the correct answer is C • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to \$200

Available with Beat the GMAT members only code

### Top First Responders*

1 Jay@ManhattanReview 70 first replies
2 fskilnik@GMATH 50 first replies
3 Brent@GMATPrepNow 50 first replies
4 GMATGuruNY 33 first replies
5 Rich.C@EMPOWERgma... 27 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 fskilnik@GMATH

GMATH Teacher

106 posts
2 Brent@GMATPrepNow

GMAT Prep Now Teacher

94 posts
3 Max@Math Revolution

Math Revolution

93 posts
4 Jay@ManhattanReview

Manhattan Review

82 posts
5 GMATGuruNY

The Princeton Review Teacher

77 posts
See More Top Beat The GMAT Experts