A librarian has a set of seven books, including four different books about Abraham Lincoln. The librarian wants to put the seven books on a shelf with the four Lincoln books next to each other, somewhere on the shelf among the other three books. How many different arrangements of the seven books are possible?
Pick one
A) (7!)/(4!) B) (4!)(3!) C) (4!)(4!) D) (4!)(7!) E) (4!)(3!)(7!)
You can club the four Lincoln books as one, which leaves us with three other books plus this one to think about. So, these four items can be arranged in 4! 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 4!*4!, which is (4!)(4!).
<result>C</result>
A librarian has a set of seven books, including four different books about Abraham Lincoln. The librarian wants to put the seven books on a shelf with the four Lincoln books next to each other, somewhere on the shelf among the other three books. How many different arrangements of the seven books are possible?