Grades 6–8Discrete MathematicsPlanned
Counting principles
The addition and multiplication principles, ordered arrangements (permutations), factorial notation and complementary counting.
math.discrete.counting-principles
The lesson for this topic has not been written yet. The outline below is part of the curriculum map and has not been reviewed.
Builds on
Required prerequisites, all the way down: 5
You will learn to
- Apply the addition and multiplication principles to count outcomes.
- Count arrangements of n objects (n!) and ordered selections of k objects from n.
- Use complementary counting, for example to count passwords containing at least one digit.
Definition
- n! = n × (n − 1) × ⋯ × 1 for n ≥ 1, and 0! = 1.
- A permutation is an ordered arrangement of objects.
Theorem
- Addition principle: if A and B are disjoint finite sets, |A ∪ B| = |A| + |B|.
- Multiplication principle: |A × B| = |A| · |B|.
- The number of ordered selections of k objects from n distinct objects is n!/(n − k)!.
Common misconceptions
- Adding where the multiplication principle applies, or multiplying where the addition principle applies.
- Counting overlapping cases twice.
Leads to
Optional discoveries
- Probability Counting equally likely outcomes gives probabilities.