Number of monic polynomials = $q^n$?

Question

In the situation $q=p^k$ with $p$ prime and $k \in \mathbb{N}$ I have the following question:

Why is the number of monic polynomials of degree $n$ in $\mathbb{F}_q[X]$ $$q^n \ ?$$

Answer 1

I think you've never read an explanation, because it is probably considered obvious.

Monic polynomials of degree $n$ look like $x^n + a_{n-1} x^{n-1} + \dots + a_1 x + a_0$. How many options are there for each of the $a_i$?