Problemas de contagem e o princípio da inclusão e exclusão

Abstract

In this work we approach the main counting techniques. We explore some properties of Pascal's triangle and his relationship with Newton's binomial. In addition, we present the Kaplansky's lemmas, the Dirichlet's principle, the proof and applications of the Principle of Inclusion and Exclusion. The methodology is applied at some problems of probability, geometry, elementary number theory and arithmetic progressions. These applications are relevant to motivate the use of counting methods in the high school curriculum and in other branches of mathematics.