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

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Mike@Magoosh: GMAT Instructor; Posts: 768; Joined: Wed Dec 28, 2011 4:18 pmFollowed by: 140 members; Location: Berkeley, CA; Thanked: 387 times

by Mike@Magoosh » Tue Jan 20, 2015 10:45 am

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!)

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https://magoosh.com/gmat/2015/counting-p ... -the-gmat/

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Source: Beat The GMAT — Problem Solving | Tue Jan 20, 2015 10:45 am

GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Thu Jan 29, 2015 5:09 am

Mike@Magoosh 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!)

Step 1) Consider the 4 books of Abraham Lincoln as ONE ENTITY and Treat it like a book.

Step 2) Now we have 7 different entities (6 books and one Group entity) which can be arranged in a row in
7 x 6 x 5 x 4 x 3 x 2 x 1 = 7! ways

Step 3) However the Group entity has 4 books which can be arranged in 4x3x2x1 = 4! ways within the group

Therefore Total ways of arrangements of all the books = 7! x 4!

Answer: Option C

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