Question

Solving Permutations and Combinations. In how many ways can seven books be arranged on a shelf if the books are different and four particular books must be together?

If possible, also please provide more tips. Thanks.

Answer 1

24

Explanation:

We have 7 books that are all different, but let's say that we have a series of 4 books (let's go with The Hobbit and the 3 volumes of the Lord of the Rings) and they have to be arranged in order (Hobbit, Fellowship, Two Towers, and Return for short). How many ways can we arrange the books?

Let's first look at our set of 4 books. They can only be arranged one way. So where can we put these books? They could be in book spots 1-4 (with the other 3 spots going to the other 3 books). Or in spots 2-5. Or 3-6. Or ever 4-7. In total there are 4 places these books can go.

The other 3 books can be arranged in any which way, and so we express that as `3! = 6`.

In total, there are:

`4xx6=24` ways to arrange the books.