Just about everything that a non-specialist in combinatorics needs to know about counting can be found in Rota's twelvefold way, which lists the 12 counting pro

Just about everything that a non-specialist in combinatorics needs to know about counting can be found in Rota's twelvefold way, which lists the 12 counting problems that you can define for finite sets and shows how to solve them: https://en.wikipedia.org/wiki/Twelvefold_way https://en.wikipedia.org/wiki/Twelvefold_way This also takes care of most of discrete probability.