Why do I keep choosing the wrong probability rule? I was wondering if someone could help clarify probability rules, although I think I understand them, whenever I have a straight forward and/or probability question, I seem to want to do a permutation or combination. For example...using the numbers 1-7 form a 4 digit number without repeats. When I saw this I immediately wanted to do a permutation of 7P4, only to find out that it is 7*6*5*4. I hope this isn't too simple or vague a question, thanks in advance.

The value $_7P_4$ and $7 \cdot 6 \cdot 5 \cdot 4$ are the same.
The $P$ stands for permutations, which is exactly what you want, because $7612$ is distinct from $1267$.
If it were
$$_7C_4 = \frac{7!}{4!(7-4)!}$$
then these would be combinations, and would be incorrect for this question because the order of the digits does matter here.
But what you have is correct:
$$_7P_4 = \frac{7!}{(7-4)!} = 7 \cdot 6 \cdot 5 \cdot 4.$$
