Order matters, repetition allowed

How many words of length $k$ can be formed from the letters of an $n$ letter alphabet?

• There are $n$ ways to select the first letter.
• $n$ ways to select the second.
• $n$ ways to select the $k$th letter.

So by the product rule, the overall number is:

$$\stackrel{k}{\overbrace{n\cdot n\cdot ...\cdot n}}=n^k$$