Counting Principles

Permutations and combinations

Learning Objectives
Discussion Starters
Differentiation Ideas
Presentation Mode

lessons (2)

1

Introduction to Permutations

Learn how to count arrangements where order matters using permutations.

Advanced25 minTeacher View
2

Introduction to Combinations

Learn how to count selections where order doesn't matter using the combinations formula.

Advanced25 minTeacher View

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 Students Will 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.