Question

A bookcase has 9 shelves and each shelf has m books in it. Harsh arranges 4 books in the bookcase and takes out 9 books. If 58 books are left in the bookcase, how many books are in each shelf?

Answer 1

Answer:

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