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GMAT Club 12 Days of Christmas is a 4th Annual GMAT Club Winter Competition based on solving questions. This is the Winter GMAT competition on GMAT Club with an amazing opportunity to win over $40,000 worth of prizes!
20 Jan 2015, 11:46
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
70% (01:10) correct
30%
(01:15)
wrong
based on 347
sessions
History
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Time
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Not Attempted Yet
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:
https://magoosh.com/gmat/2015/counting-p ... -the-gmat/
Mike
(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:
https://magoosh.com/gmat/2015/counting-p ... -the-gmat/
Mike
20 Jan 2015, 15:29
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mikemcgarry
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:
https://magoosh.com/gmat/2015/counting-p ... -the-gmat/
Mike
(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:
https://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.
General Discussion
24 Aug 2018, 07:23
Kudos
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mikemcgarry
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:
https://magoosh.com/gmat/2015/counting-p ... -the-gmat/
Mike
(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:
https://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
