Writing expressions using permutations versus combinations

This question states a PMF using combination notation, and the numerator of the expression is actually equal to a permutation:$$\frac{\binom{365}{k}k!}{365^k}$$

I have been trying to write permutations using latex, and I find that it is quite awkward.Question: Is the math written in combinations because that is the preferred option to express the logic or because permutations are difficult to create in LaTeX/Stackexchange.

Note: You might think this trivial, but I am trying to understand. Should I think in "combinations" or "permutations"?