Subjective and objective approaches in solution of the problems of probability theory and discrete mathematics

The article considers and analyzes the main types of errors made by students in solving the problems of probability theory related to the concept of a random event, as well as the problems of such branches of discrete mathematics as combinatorics, theory of sets, logistics. We have compared the subjective and objective approaches to solving this problems, gave their detailed solutions and methodical recommendations for teachers on improvement of the teaching process. The article can be useful for teachers of mathematics and specialists dealing with discrete and stochastic methods for solving problems, as well as for students studying these branches of probability theory and discrete mathematics.