The aim of this lecture is to strengthen the knowledge (theorems and formulas) which we have presented in the previous section. This time we focus mainly on applications of these combinatorics ideas and also introduce some new problems like counting relations, especially the equivalence relation. We devote a bit of time to the cardinality of the union of sets  as well as to the Dirichlet's box principle.
Notice, that these lecture's issues are well discussed in a book by Lipski W. "Combiantorics for programmers", WNT, 1982. Even though the scope of this book goes beyond our considerations, we encourage you to familiarize yourself with it. Another publication worth reading, which is much math-oriented, was written by Graham R., Knuth D., Patashnik O., "Concrete mathematics", Addison-Wesley Pub. Comp. 1994. "Discrete mathematics" by Ross K., Wright Ch. includes an excellent introduction to the Dirichlet's box principle with its many interesting and surprising applications (some of them we consider in our lecture).