Counting Principles
Permutations and combinations
Start with the basics and progress through 2 lessons. Each lesson builds on the previous one.
0 of 2 lessons done
Test Your Knowledge
10 questions, new mix each time (from 34)
In This Topic (2 lessons)
Introduction to Permutations
Learn how to count arrangements where order matters using permutations.
Introduction to Combinations
Learn how to count selections where order doesn't matter using the combinations formula.
Counting principles provide systematic methods for counting outcomes without listing them all. The fundamental counting principle, permutations, and combinations are essential for calculating probabilities in complex situations.
What You'll Learn
- Apply the fundamental counting principle
- Calculate permutations
- Calculate combinations
- Distinguish permutations from combinations
- Solve counting problems
Frequently Asked Questions
What is the fundamental counting principle?
If you have m ways to do one thing and n ways to do another, you have m × n ways to do both. This extends to any number of independent choices.
When do I use permutations vs combinations?
Permutations: ORDER MATTERS (arranging, ranking, passwords). Combinations: ORDER DOES NOT MATTER (selecting, choosing teams, committees).
What are the formulas?
Permutation: $P(n,r) = \frac{n!}{(n-r)!}$. Combination: $C(n,r) = \frac{n!}{r!(n-r)!}$. Combinations are smaller because we divide by r! to remove ordering.