Often, in practice, exists the following problems: choosing from a multitude
of sub-multiple objects of elements that possess certain properties; to arrange the
elements of one or more sets in a certain order; to determine the number of all subsets
of a set, set up according to certain rules. The paper examines the following aspects:
• analysis of application the elements of the combinatorics;
• analysis of the application of permutations, combinations, arrangements to solve some
practical problems;
• development a software to solve these problems.
A number of typical examples were investigated:
• generation of permutations, combinations, arrangements;
• calculating the number of variants for generating the distinct numbers, made up of some
figures indicated;
• diversifying the composition of the delegations;
• formation of dance pairs;
• arranging the meal in a room in the student apartment
• etc.