$7$ nouns, $5$ verbs, and $2$ adjectives are written on a blackboard. We can form a sentence by choosing $1$ from each available set in any order. Without caring it makes sense or not, what is the number of ways of doing this?
If we use a permutation and just do $7 \cdot 5 \cdot 2$, it gives us $70$. But the problem states that the sentence can be in any order. I am confused exactly how I am supposed to figure out the number of possibilities. Would you multiply $70$ by the number of possible arrangements? If so, what is that number?