Question

A librarian has a set of ten different 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 different 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!)

Answer 1

B

Explanation:

The first thing the man needs to do

Is to arrange the books by Abraham Lincoln amongst each other first. Now the number of ways the man can arrange these books amongst each other is a total of 4! Ways. Now there are 6 books remaining and there are also six slots remaining. The number of ways to arrange these six books within theirselves would be 6!

Now the total

Number of arrangements is 6! * 4!