Galois group is $S_n$ then $L$ is the splitting field of a degree $n$ polynomial

Question

I am revisiting Galois Theory and am faced with the following problem.

Let $L/K$ be a finite Galois extension whose Galois group is isomorphic to $S_n$. Show that L is the splitting field of a separable polynomial of degree $n$.

My idea, is that since the extension is normal, we know $L = $ Split$_K(f)$ for some $f\in K[X]$, so we want to use Orbit-Stabilizer or something to show $deg(f) = n$.