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

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Magoosh GMAT Instructor
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A librarian has a set of ten books, including four different books abo  [#permalink]

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New post 20 Jan 2015, 11:46
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C
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E

Difficulty:

  35% (medium)

Question Stats:

66% (00:43) correct 34% (01:03) wrong based on 120 sessions

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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 OE for this particular question, see:
http://magoosh.com/gmat/2015/counting-p ... -the-gmat/

Mike :-)

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Re: A librarian has a set of ten books, including four different books abo  [#permalink]

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New post 20 Jan 2015, 15:29
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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!)


For a set of Counting Practice Problems for the GMAT, as well as the OE for this particular question, see:
http://magoosh.com/gmat/2015/counting-p ... -the-gmat/

Mike :-)


Hi Mike,

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.
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Re: A librarian has a set of ten books, including four different books abo  [#permalink]

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New post 24 Aug 2018, 07:23
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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!)


For a set of Counting Practice Problems for the GMAT, as well as the OE for this particular question, see:
http://magoosh.com/gmat/2015/counting-p ... -the-gmat/

Mike :-)


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
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Re: A librarian has a set of ten books, including four different books abo &nbs [#permalink] 24 Aug 2018, 07:23
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