Lecture on the topic: Combinatorics Lecture plan Combinatorics as a science Combinatorics is a branch of mathematics that studies questions about how many combinations of a certain type can be made from given objects (elements). The birth of combinatorics as a branch of mathematics is associated with the works of B. Pascal and P. Fermat on the theory of gambling. Interest in combinatorics revived in the 1950s due to the rapid development of cybernetics, planning theory and information theory. Sum rule Let there be n pairwise disjoint sets of containing elements, respectively. The number of ways in which one element can be chosen from all these sets is Example . The course has 3 groups. There are 25 people in the first one, 30 people in the second one, and 20 people in the third one. In how many ways can one student be chosen from them? Example . The course has 3 groups. There are 25 people in the first one, 30 people in the second one, and 20 people in the third one. In how many ways can one student be chosen from them? Example . The course has 3 groups. There are 25 people in the first one, 30 people in the second one, and 20 people in the third one. In how many ways can one student be chosen from them? Solution: elements, respectively. From the first group, one person can be chosen in 25 ways, from the second - 30 , from the third - 20 . To find the answer, you need to add all these ways: 25+30+20=75 . Thus, there are 75 ways to choose one student from three groups.
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