How many ways can we put 3 math books and 5 English books on a shelf if all the math books must stay together and all the English books must also stay together? (The math books are all different and so are the English books.)
+6248 \(\text{The math books can be either to the left or right of the english books. That's 2 choices}\\ \text{Within the math books there are $3!$ arrangements}\\ \text{Within the english books there are $5!$ arrangements}\\ \text{The total number of arrangements is thus $2 \cdot 3! \cdot 5! = 1440$}\)
.
