Foundational Mathematics: Permutations and Combinations

Counting principles are essential for success in advanced mathematics, statistics, and computer science. This course provides a structured, text-based introduction to the powerful concepts of permutations and combinations. By the end of this course, you will move beyond simple memorization of formulas to deeply understand why and when to use permutations (arrangements) versus combinations (selections). You will gain the logical foundation needed to tackle probability questions and combinatorial analysis with confidence. What you'll learn: * Understand the fundamental counting principle (multiplication rule) and its application to sequences and events. * Master the use of factorials and the distinction between permutations with and without repetition. * Apply combination formulas to determine the number of unique ways to select items from a given set. * Practice solving word problems involving complex arrangements and constraints, including circular permutations and grouping. * Learn how permutations and combinations form the essential basis for calculating basic and conditional probability. The course begins with core terminology and the basic rules of counting before progressing through detailed explanations of permutations, combinations, and constrained arrangements. Each section includes written examples and practice problems designed to reinforce logical application. This course is designed for absolute beginners in combinatorial mathematics. No prior knowledge of permutations or combinations is required, only basic arithmetic skills. Start building your logical reasoning skills today.