Abstract
This chapter presents generalized principle of inclusion and exclusion and its applications. The principle of inclusion and exclusion is very important and useful for enumeration problems in combinatorial theory. By using this principle, in the chapter, the number of elements of A that satisfy exactly r properties of P are deduced, given the numbers of elements of A that satisfy at least k ( k ≥ r) properties of P. In the chapter, a method is described to deduce the number of elements of A that satisfy exactly r i properties of the i th group of properties (1 ≤ i ≤ n ) if the properties in the principle problem are divided into n groups and r 1 , r 2 , . . . . r n are n integers.
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