This is just a question to make sure I understand the intuition of using combinations to calculate probabilities from examples such as a deck of cards. Take for example finding the probability of a full house. Is the logic as follows, at the end of the day we are defining the probability as the number of hands/outcomes in the sample space that satisfy the desired condition(i.e. the total number of outcomes that give a full house), over the total number of outcomes/cardinality of the sample space itself? so instead of literally enumerating all possible outcomes, and then counting the total and counting all the possible combinations of full houses by hand, we can use the counting rules to do so?
When are there restrictions on this- can we use this definition of probability more broadly and then use counting tools or does it only apply to cases where the support is finite and each individual outcome equally likely?