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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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Question Stats:

64% (01:12) correct 36% (01:21) wrong based on 255 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  [#permalink]

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New post 23 Dec 2018, 17:51
Hi,

I am not getting one thing in both the answer, question states they have 4 different book of AB Li then how you can count them as one?

GMATPrepNow aviram mikemcgarry
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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 11 Jan 2019, 08:25
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Gmatprep550 wrote:
Hi,

I am not getting one thing in both the answer, question states they have 4 different book of AB Li then how you can count them as one?

GMATPrepNow aviram mikemcgarry


We are treating the 4 Abraham Lincoln as different.
There are 4! ways (24 ways) to arrange these 4 books in a row.
Once we arrange these 4 different books in a row, we "glue" them together so that we can ensure that they stay together. Those 4 books are still different books, they are just glued together.
Does that help?

Cheers,
Brent
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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 11 Jan 2019, 08:50
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Gmatprep550 wrote:
Hi,

I am not getting one thing in both the answer, question states they have 4 different book of AB Li then how you can count them as one?

GMATPrepNow aviram mikemcgarry


Hey Gmatprep550 ,

Well it is a way to make your life easier , you consider those 4 books as an single entity so that you can address the problem in an easier way ,remember that they have to be next to each other.
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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 21 Jan 2019, 18:45
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!)


Since the 4 Lincoln books must be together, we can, for now, treat them as just 1 book. Since there are 6 other books, there are 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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Re: A librarian has a set of ten books, including four different books abo   [#permalink] 21 Jan 2019, 18:45
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