History of Science and Engineering Annotation << Back THEORETICAL BASES ELEMENTARY COMBINATORICS. FORM-ING AND DEVELOPMENT А.Е. Malykh E.I. Yankovich On the basis of analysis of numerous sources historical process of formation different approaches to solution concrete practical problems of combinatorial nature is uncovered. Arising of ways and rules for finding the set of decisions for problems of the same type is shown. Search process for obtaining general and recurrent formulae for counting known to that time kinds of combinatorial combinations with repeating (bounded and with out restriction) and with out of repeating their elements is described. Such complexes were: all possible permutations from n elements , where n1+n2+…+nk=n); combinations of n elements m at a time – unordered m-subsets of n-set; arrangements – ordered m-subsets of n-set The ways of solution such problem by different peoples to XVII century is shown. Among them were scientists from China, India, countries of Islam, Jews, mathematicians of medieval Western Europe. Scientific contrihution of scholars that period in formation of combinatorics is estimated. Key words: elementary combinatorics, arrangements, permutations, compositions; combinations with repeating elements; counting for-mulae. Contacts: E-mail: malych@pspu.ru E-mail: LenuMF@mail.ru Pp. 12-21.