I've got a number of books and resources for statistics theory, but I've always had problems with the approaches needed in answering questions, specifically for probability theory where counting techniques are needed. For instance, I've got one problem right here where for a 52-card deck, you pick a hand of 10, so what is the probability that 3 will be aces?
When I see these problems, I am always second-guessing the approaches needed to take to find the answer and never feel I understand it. Unfortunately all the books I have only give a few such examples and then move on, leaving me still without a concrete understanding. I'm wondering if there are is a good resource or two that specifically tackles these type of problems, and offers an abundant set of exercises for getting to the bottom of it?
It doesn't need to go so far as differing between types of distributions, significance tests, etc., but just some concrete and thorough way to explain the number theory, recognizing problems that require it, and appropriate ways of implementing it.