Find how many different ways you can wallpaper 8 rooms

Question

What are the steps in the solving the problem below. Do you use the product rule, summation rule, or both?

In how many ways you can wallpaper the same $8$ rooms with $12$ types of wallpaper?

Answer 1

Let's assume you can reuse a wallpaper. Then for each room there are 12 possibilities, so by the product rule there are $12^8$ possibilities in total.

Answer 2

Repetition allowed: $12\cdot12\cdot12\cdot12\cdot12\cdot12\cdot12\cdot12=12^8$.

Repetition not allowed: $12\cdot11\cdot10\cdot9\cdot8\cdot7\cdot6\cdot5=\frac{12!}{(12-8)!}$.