About teaching students to methods of solving problems by combinator

Eshim Murotovich Mardonov (Ph.D., Associate Professor, SamSU Samarkand city)
Kurbon Ostanov (Ph.D., Associate Professor, SamSU Samarkand city)
U Achilov (Samarkand State University)

Indonesian Journal of Education Methods Development
Vol. 8 (2019): November

This article reveals some aspects of the formation of skills to solve combinatorial problems when studying a school course in mathematics. It also considers methods for solving historical combinatorial problems, combinatorial problems and the rule of multiplication, developing skills for solving combinatorial problems, tasks on forming concepts, a tree of options, factorial, applying equations to equations and simplifying expressions, combinatorial problems for studying the concepts of permutations without repetitions, permutations with repetitions, placements without repetitions, placements with repetitions, combinations without repetitions, combinations with repetitions. In mathematics, there are many problems that require elements make available a different set, count the number of all possible combinations of elements formed by a certain rule. Such problems are called combinatorial, and the branch of mathematics involved in solving these problems is called combinatorics. Some combinatorial problems were solved in ancient China, and later in the Roman Empire. However, as an independent branch of mathematics, combinatorics took shape in Europe only in the 18th century. in connection with the development of probability theory. In ancient times, pebbles were often used to facilitate calculations. In this case, special attention was paid to the number of pebbles that could be laid out in the form of a regular figure. So square numbers appeared (1, 4, 16, 25, ...). In everyday life, we often face problems that have not one, but several different solutions. To make the right choice, it is very important not to miss any of them. To do this, iterate through all possible options. Such problems are called combinatorial. It turns out that the multiplication rule for three, four, etc. tests can be explained without going beyond the plane, using a geometric picture (model), which is called the tree of possible options. It, firstly, like any picture, is visual and, secondly, it allows you to take everything into account without missing anything.