Question

Question #4cce4

Answer 1

(a) `36`
(b) `12`

Explanation:

Problem (a)

Three particular books can be put together in `3! = 6` ways.

With each of these we can put the other two books either before them (`2! = 2` ways) or after them (`2! = 2` ways), or one before and one after (`2! = 2` ways). So, there are `2+2+2=6` ways of positioning the other two books.

Therefore, the total number of ways `5` books can be put on a shelf with three particular books to be next to each other equals to `6*6=36`.

Problem (b)

The two biggest books can be positioned at each end of a set of `5` books in `2! = 2` ways.

With each of them the other three books can be positioned between them in `3! = 6` ways.

Therefore, the total number of ways `5` books can be put on a shelf with two biggest book to be at each end if `2*6=12`