This trusted best-seller covers the key combinatorial including the pigeon-hole principle, counting techniques, Permutations and Combinations, pólya counting, Binomial coefficients, inclusion-exclusion principle, generating functions and recurrence relations, combinatorial structures (matching, designs, graphs), and flows in networks. The 5th edition incorporates feedback from users to the exposition throughout and adds a wealth of new exercises. features: 1) covers a wide range of topics: -dilworth's theorem -partitions of Integers -counting sequences and generating functions -Extensive graph theory coverage 2) a clear and accessible presentation, written from the student's perspective, facilitates understanding of basic concepts and principles. 3) An excellent treatment of pólya’s counting theorem that does not assume students have studied group theory. 4) many worked examples illustrate methods used. table of Contents: \nChapter 1. What is combinatorics \nChapter 2. The pigeonhole principle \nChapter 3. Permutations and Combinations \nChapter 4. Generating Permutations and Combinations \nChapter 5. The Binomial coefficients \nChapter 6. The inclusion-exclusion principle and applications \nChapter 7. Recurrence relations and generating functions \nChapter 8. Systems of distinct representatives \nChapter 10. Combinatorial designs \nChapter 11. Introduction to graph theory \nChapter 12. More on graph theory \nChapter 13. Digraphs and networks Chapter 14. Pólya counting