Теория вероятностей #4: Комбинаторика / задачи с и без замещения, учет порядка, комбинации в покере

In this video, we'll examine the most historically ancient application of probability theory—combinatorial problems. We'll discuss in detail what constitutes a combination, which problems are considered problems with and without substitution, what algorithms exist for counting the number of combinations, whether the order of elements in a combination is important, what are permutations, combinations, and arrangements, and what role does the presence of repeating objects in the original set of objects that make up a combination play. We'll present almost all of the material here through examples, many of which come from games of chance—they were the primary motivation for philosopher-mathematicians of the 17th and 18th centuries to discuss the nature of randomness and seek solutions to the first probability problems. 0:00 Start 2:50 What is a combination? 4:17 Object Selection Problems with Replacement 5:45 Object Selection Problems without Replacement 7:11 Taking Order into Account When Counting Combinations 9:14 Combination Examples (Ticket Number, Die Rolls, Poker Combinations) 13:24 Counting Combinations: Multiplication Rule 14:44 Basic Counting Formulas (With/Without Replacement, With/Without Order) 17:37 Deriving Counting Formulas Using the Ticket Number Example 30:23 Counting Example: Poker Combinations 43:29 The Importance of Distinguishability and Indistinguishability of Objects: Red and Blue Ball Example 48:33 Counting Permutation Numbers When There Are Indistinguishable (Repeating) Objects 50:18 Example of Counting Permutations with Repetitions (Football Season) Follow our A Telegram channel where additional materials, information about new courses, news from the world of mathematics and data science, and much more are posted: https://t.me/getsomemath Contacts: http://apershin.com