COMBINATORY PROBLEMS AND THEIR SOLUTION METHODS

this article reveals the features of teaching students methods of solving problems in combinatorics when studying a school course in mathematics, and also considers methods for solving historical combinatorial problems, problems on the multiplication rule, developing skills in solving problems on the formation of combinatorial concepts, tree of options, factorial, application to solving equations and simplifying expressions. When discussing formulas for figured numbers, it is proposed to give students tasks to independently find a pattern and verify their correctness for specific values of a natural variable, and then solve problems using a formula to find a certain number by location and type of number; inverse problems by number to find what type a given number belongs to, when discussing solving problems similar to the well-known problem, in which it is required to find the number of possible seating positions by people, the number of which is equal to the number of seats, it is indicated to first number the seats, and then find the number of permutations of seating of these seats by people.