Where can I learn the basics of combinatorics? I'm in last year at high school and I want to enter a computer science college, my problem is that I wasn't taught any combinatorics in high school and that's a heavy subject in my admission exam. Maybe anyone can provide me some links with combinatorics problems solved and explained or some book....
 A: Combinatorics is often taught as a sophomore undergraduate course in my experience and not often directly taught as a highschooler (except for maybe basic counting principles).
Regardless, here is a list of books that I either learned from or know of that might suit your needs.
Introductory Combinatorics by Brualdi was the first text that I studied the subject from.  It is rather clear, even from the first time seeing the subject and covers many topics.
Finite Mathematics and its Applications by Goldstein, Schneider, and Siegel is a book used for our freshman undergraduates who are not in a STEM field.  Only a few chapters are dedicated to counting problems, but it should cover everything that I would expect should be known by highschoolers.  Much of the rest of the book covers topics such as introductory uses of matrices and mathematical finance, but those which are dedicated to combinatorics have simple examples that should be easily understood (perhaps too simple).
Discrete Mathematics with Graph Theory by Goodaire and Parmenter is a book that our college uses for its undergraduate combinatorics classes for non-math majors.  When I TA'd the course, the students were almost entirely industrial engineering majors.  This book focuses on how to write proofs for the first few chapters and then continues to topics in combinatorics.  Many good examples.
Applied Combinatorics by William Trotter is a book that our college uses for its undergraduate combinatorics classes for math majors.  It is available free under a creative commons license.  It may be difficult as a first introduction if you have not yet had a class on set theory, but the prerequisites on the course catalog only go so far as integral calculus.
Concrete Mathematics by Graham, Knuth, and Patashnik I have not ever used in a classroom setting, but I have enjoyed reading it to supplement my knowledge and list of examples.  A bit harder than the other texts, this one is especially good in regards to giving challenging problems that might or might not be solvable the first time you read the book.  Problems are labeled in difficulty ranging from the trivial and mundane to research appropriate topics.  Despite this, things are explained well and should still be accessible to a first time student of the subject.  Just don't be discouraged if you can't solve all the problems.
In addition to these, a number of other good books are mentioned in the thread: Good Book On Combinatorics
