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?

Answer 1

120960

Explanation:

Given that 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.

First arrnage the 6 other books in the shelf.

This can be done in
`6! ways`

Now arrange the 4 books of Lincoln

This can be done in
`4! ways`

Now we have 7 places to insert Lincoln books including two corners and in between.

Thus this can be done in 7 ways

Total no of ways =
`6!(4!)(7) = 120960`