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A librarian has a set of ten books, including four different books abo
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17 Aug 2022, 11:16
17 Aug 2022, 11:16
Expert Reply
00:00
Question Stats:
81% (00:54) correct
18% (01:00) wrong based on 16 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!)
(A) (10!)/(4!)
(B) (4!)(6!)
(C) (4!)(7!)
(D) (4!)(10!)
(E) (4!)(6!)(10!)
Part of the project: GRE QCQ & PS 3 Questions Every One DAILY Challenge - (2022)
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GRE Math Essentials (2022)
GRE Geometry Formulas
GRE - Math Book
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GRE Math Essentials (2022)
GRE Geometry Formulas
GRE - Math Book
Re: A librarian has a set of ten books, including four different books abo
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17 Aug 2022, 11:24
17 Aug 2022, 11:24
Carcass, can you please clarify why B is not correct?
Re: A librarian has a set of ten books, including four different books abo
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17 Aug 2022, 11:43
17 Aug 2022, 11:43
1
Expert Reply
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
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
