Basic Counting Examples

Combinatorics · Axiom Academy

EXAMPLE Basic Counting Examples Master fundamental counting principles through step-by-step problem solving Problem 1: Three-Digit Numbers with Distinct Digits Excellent work! You've mastered these fundamental counting principles: Multiplication Principle: When making sequential choices, multiply the number of options at each step to find the total number of outcomes. Permutations vs Combinations: Permutations (arrangements) care about order, while combinations (selections) do not. Use n! for permutations and C(n,r) for combinations. Without Replacement: When items can't be repeated (distinct digits, different people), reduce the available choices at each step. Independent Choices: When choices in different categories are independent (like letters and digits), multiply the possibilities for each category. Strategic Thinking: Break complex problems into simpler sequential decisions, then apply the appropriate counting rule. These fundamental principles form the foundation for more advanced combinatorics. Practice identifying when to use multiplication, permutations, or combinations!

This is the written version of the interactive lesson above. See the full Combinatorics course.