Let $S$ be a string $|S|$ its length. Let $\Sigma$ be an alphabet and $|\Sigma|$ its size. Both $|S|,|\Sigma| \in \mathbb{Z}^{+}$. Let $S[i,i+k-1]$ be a substring and $|S[i,i+k-1]|=k$ its size.

how does one prove that the highest number of different substrings of size $k$ is $|\Sigma|^{k}$

it is obvious but what i am looking for is the reasoning that gets me from $S[i,i+k-1]$ to $|\Sigma|^{k}$.

thank you