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

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