A librarian has a set of twelve books, including four different books about Abraham Lincoln. The librarian wants to put the twelve books on a shelf with the four Lincoln books next to each other, somewhere on the shelf among the other eight books. How many different arrangements of the twelve books are possible? Options:
A) (12!)/(4!)
B) (4!)(8!)
C) (4!)(9!)
D) (4!)(12!)
E) (4!)(8!)(12!)
You can club the four Lincoln books as one, which leaves us with eight other books plus this one to think about. So, these nine items can be arranged in 9! 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 9!*4!, which is (4!)(9!).
<result>C</result>
A librarian has a set of twelve books, including four different books about Abraham Lincoln. The librarian wants to put the twelve books on a shelf with the four Lincoln books next to each other, somewhere on the shelf among the other eight books. How many different arrangements of the twelve books are possible?