Question

Choose the correct option.
What are the number of ways of arranging 9 books out of 14 in a library where the librarian, while arranging the books, zot
2 damaged books and sent them for rebinding and repairing?​

Answer 1

Step-by-step explanation:

Put one of the two particular books to one side.

Then there are

8

books to arrange in any order on the shelf.

There are

8

choices for the first book,

7

for the next,

6

for the next, etc.

So there are:

8

!

=

8

×

7

×

6

×

...

×

1

=

40320

ways to arrange the

8

books.

Then you can place the reserved book on either side of its companion. So for each of the possible

40320

ways to arrange the other

8

books, there are

2

possible acceptable arrangements of

9

books.

So the number of acceptable arrangements of the

9

books is:

8

!

⋅

2

=

80640