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

Source: Magoosh

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!

The OA is C.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Wed Aug 15, 2018 5:21 pm

BTGmoderatorLU wrote:Source: Magoosh

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 side-by-side, place them in a BLOCK:
[Lâ‚�Lâ‚‚Lâ‚ƒLâ‚„].
Consider this 4-book block a single element to be arranged with the other 6 books.
The number of ways to arrange the Lincoln block and the other 6 books -- a total of 7 elements -- is 7!.
Since the 4 books within the Lincoln block can swap positions, we multiply by the number of ways the 4 books within the Lincoln block can be arranged (4!):
4!7!.

The correct answer is C.

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swerve: Legendary Member; Posts: 2229; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

by swerve » Thu Aug 16, 2018 9:22 am

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. Regards!

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Scott@TargetTestPrep: GMAT Instructor; Posts: 7247; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Thu Aug 23, 2018 3:52 pm

BTGmoderatorLU wrote:Source: Magoosh

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, pretend that they are just 1 book. Since there are 6 other books, there is 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

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Fri Aug 24, 2018 6:23 am

BTGmoderatorLU wrote:Source: Magoosh

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!

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

Brent Hanneson - Creator of GMATPrepNow.com

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