This thesis presents a comprehensive overview of the historical evolution of combinatorics into a separate branch of mathematics. Within the educational framework, the appreciation for the historical and cultural dimensions of mathematics stands as a prominent goal. Listed within are also the learning outcomes derived from the integration of combinatorial principles into teaching methodologies. The initial focus centers on the foundational topic of counting principles, with subsequent analyses delving into the principles of multiplication, sum, difference, and quotient. Each principle is explicated through illustrative problems sourced from high school textbooks, enhancing clarity and comprehension. Extending beyond the basics, the thesis defines the concepts of permutations, variations, and combinations, considering both repetitions and non-repetitions. Accompanying these definitions are practical examples showcasing the application of these concepts. Additionally, a compilation of problems from national mathematics competitions enriches the illustrative repertoire. Towards the conclusion, the thesis provides examples of teaching activities. The first activity, tailored for elementary school students and employing visual aids, aims to describe the multiplication principle. For high school students, a challenging problem from the county level of the national mathematics competition is incorporated into one of the teaching activities, fostering the recognition and application of diverse problem-solving methodologies through four distinct approaches