We have n factorial (n!) ways to arrange n different things in a sequence.
1440 ways
Practice makes perfect
We want to arrange 5 different French books and 3 different Spanish books on a shelf, making sure that all books of the same language remain together. Within each such arrangement we either have Spanish books before the French ones, or the French ones before the Spanish ones.
SpanishFrench or FrenchSpanish
Now, recall that n factorial (n!) gives us the number of ways to arrange n different things in a sequence. Let's use this fact to find how many ways we have to arrange the books in each language.
5French books ⇒ 5! ways to arrange them
3Spanish books ⇒ 3! ways to arrange them
We have 2 ways to order the languages, 5! ways to order the French books and 3! ways to order the Spanish books. Since each ordering is independent of the others, the total number of ways in which we can order the books is the product of these numbers.
2 * 5! * 3!
Finally, let's find the value of this expression.
