The manual discusses the classical enumeration problems of choosing and ordering elements of a finite set and the problem of dividing finite sets and multisets. The basic concepts, facts and methods of enumerative combinatorics are given in the volume that allows a university graduate at a high substantive and methodological level to develop and conduct elective and elective courses in combinatorics in high school. The material presented is also the foundation for the study of "serious" educational and monographic literature on combinatorics and its applications.