“APPLICATIONS IN TEACHING THE FUNDAMENTALS OF COMBINATORICS IN GENERAL SECONDARY SCHOOLS”

Аннотация

In this article discussed that, importance of interdisciplinary integration, some of the requirements and conditions for the introduction of integrated education in the primary grades, and described in detail thegeneral features oftheintegrated course. Keywords: placements, enterprises, integration, interdisciplinary integration, educational effectiveness, primary education, integration lessons. ANNOTATSIYA: Ushbu maqolada fanlararo integratsiya, boshlang‘ich sinflarda integratsion ta’limni yo‘lga qo‘yishning ayrim talab va shartlari yoritilgan bo‘lib, integratsion darsning umumiyxususiyatlari atroflicha bayon etiladi. Kalit so'zlar: O’rinlashtirishlar, kombinatorika, integratsiya, fanlararo integratsiya, ta'lim samaradorligi, boshlang‘ich ta’lim, integratsion darslar. Introduction. As you know, no one can predict and say in advance the events taking place in nature. For example, what will the weather be like in Tashkent in a week? Of course, no one can say this for sure. But you can find out this information on the Internet. What is this information based on? There is a branch of mathematics that deals with these issues. It is called “probability theory”.The initial concepts ofprobability theory are concepts such as experience and event. The initial concepts of probability theory are concepts such as experiment, event, elementary event, probability. An experiment is an activity that produces an event. For example, tossing a coin is an experiment. The results of the experiment are the events of the coin landing on the “heads” or“tails” side. Statistical definition of the probability of an event. Consider the following approximation. A cube-shaped playing stone (duck) is thrown (Figure 1). As a result of this experiment, the numbers one, two, three, four, five or six can fall out on its upper side. Each of these results is considered random. 1-picture Let's throw a dice 100 times and observe how many times the event "the dice lands on the number 6" occurs. Suppose that out of 100 experiments, the number 6 lands on 9 of them. In https://ijmri.de/index.php/jmsi volume 4,issue2,2025 497 theseexperiments, thenumber9is called thefrequency ofoccurrence oftheevent. The ratio of the frequency of occurrence of an event to the total number of experiments conducted is called the relative frequency of this event. In our case, the relative frequency of the event of the dice landing on the number 6in 100 experiments conducted is equal to ─.In general, a certain experiment is repeated over and over again under the same conditions, and each time the occurrence of the event A of interest to us is recorded. Suppose that the total number of experimentsis n,andin m ofthem theevent Aoccurred. In it, the number m is the frequency of occurrence of event A, and the ratio is the relative frequency of occurrence ofevent A. In general, theexperimental results show that for a large number ofexperiments conducted under the same conditions, the relative frequency of occurrence of the observed event tends to a certain stable value. It is this value that is taken as the probability of a random event. This definition is a statistical definition oftheprobability ofan event. In our coin experiment above, the probability that the coin lands on heads is is equal to . Similarly, theprobability that thecoin lands onheads is isequal to. If the occurrence of one of two events does not affect the other, such events are called independent events, Let's go back to the experiment of throwing a game stone. Let's assume that the game stone has a regular shape and is made of a homogeneous material. Based on this, when the stone is thrown, the chances of getting the numbers 1 to 6 are the same. This means that all six outcomes of the experiment (the numbers 1, 2, 3, 4, 5, and 6) are equally likely. Also, the occurrence of one of these events does not affect the other, that is, they are independent. Let us now consider the occurrence of event B, that is, a multiple of 3, when the dice are rolled. This event occurs in only two of the experiments: when the numbers 3 and 6 are rolled. We call these outcomes the favorable (favorable) possibilities for the occurrence of event B. Out of all 6 possible, equally likely outcomes, the number of favorable (favorable) possibilities for the occurrence of event B is2. The ratio of the number of all equally likely outcomes to the number of favorable (favorable) possibilitiesis called theprobability ofevent B. The classical definition of probability is the probability of a finite number of outcomes as a result of an experiment. e , e , e ,…, e Let any of the elementary events occur, and let these 1 2 3 n events form a completeset of equally likely events that are not mutually exclusive. e ,e ,...,e Suppose n ta e , e , e ,…, e from elementary phenomena m If an experiment 1 2 3 n k k k 1 2 m has n equally likely outcomes, and m of them are opportunities that favor theoccurrence of event A, then The ratio is called theprobab