It's obviously slanted towards the generating-function view of enumeration, but I enthusiastically recommend Generatingfunctionology by Herb Wilf. It covers all the topics you mentioned, written mainly in the style of examples, rather than theory---something that usually appeals to undergraduates. To me what makes the book a great introduction for a newcomer to combinatorics is Wilf's obvious enthusiasm and easy-going (yet firmly exacting) writing style. The mileage he gets out of changing a recurrence relation into a generating function is truly amazing. I think most undergraduates would be amazed that their skills in calculus can help them enumerate discrete objects, and this book does exactly that over and over again. If price matters, this one is tough to beat---the second edition is free at Wilf's website.