There's something I can not understand about proofs in combinatorics. Whenever I solve a counting problem, there's a non-negligible amount of uncertainty about the solution which I really don't feel when I solve problems in other fields, say in analysis or abstract algebra. It happens too often that someone sees my solution and tells me I've counted more or fewer than the correct answer. And I've observed this happens even to more experienced students and even teachers. But every time we come to a general agreement after refining the solution. What's wrong with me? Or does it have anything to do with how it's presented? I've never seen an axiomatic treatment of this field, like say, abstract algebra. Of course all the books I've seen start with the two counting principles, but they seem like too informal to use in rigorous proofs. Thanks in advance.