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 OA & OE for this particular question, see:
https://magoosh.com/gmat/2015/counting-p ... -the-gmat/
Mike
A librarian has a set of ten books, including four different
This topic has expert replies
GMAT/MBA Expert
- Mike@Magoosh
- GMAT Instructor
- Posts: 768
- Joined: Wed Dec 28, 2011 4:18 pm
- Location: Berkeley, CA
- Thanked: 387 times
- Followed by:140 members
Magoosh GMAT Instructor
https://gmat.magoosh.com/
https://gmat.magoosh.com/
- GMATinsight
- Legendary Member
- Posts: 1100
- Joined: Sat May 10, 2014 11:34 pm
- Location: New Delhi, India
- Thanked: 205 times
- Followed by:24 members
Step 1) Consider the 4 books of Abraham Lincoln as ONE ENTITY and Treat it like a book.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 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
"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour