Methods of solving problems for enumerating words made up of characters of a given alphabet

Abstract

Recently, tasks on the theme of "Combinatorics" have ceased to be the prerogative of Olympiad training for schoolchildren. Students learn the concepts and methods of combinatorics in informatics, mathematics, probability, and statistics courses. The task 8 of the Unified State Exam in informatics assumes that students have the ability to enumerate and calculate configurations from objects of a finite set constructed in accordance with certain rules. The article describes various methods for solving these problems: nested loops, using the itertools library, using recursive functions and recursive generator functions. The last two methods allow students to get an idea of iterated objects and better understand the structure of generator objects. Solving one problem in several ways develops criticality of thinking, has a positive effect on the creation of intrasubject connections in the studied material, and promotes deeper learning of the material.