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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
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Question Stats:
80% (00:54) correct
20% (01:00) wrong based on 15 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?
Re: A librarian has a set of ten books, including four different books abo
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17 Aug 2022, 11:43
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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!)