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Topic 1: Combinatorics

Introduction to counting techniques

4 hours

• Use the inclusion-exclusion principle formulas to determine the number of elements in the union of two and the union of three sets.
• Use the multiplication principle. 1 interactive
• Use the addition principle.

Permutations (ordered arrangements) and combinations (unordered selections)

8 hours

• Define and use permutations.
• Use factorial notation. 1 interactive
• Use the notation ⁿPᵣ to represent the number of ways of selecting r objects from n distinct objects where order is important.
• Solve problems that involve permutations.
• Solve problems that involve permutations with restrictions including repeated objects, specific objects grouped together and selection from multiple groups.
• Define and use combinations. 1 interactive
• Use the notation (ⁿᵣ) and ⁿCᵣ to represent the number of ways of selecting r objects from n distinct objects where order is not important.
• Solve problems that involve combinations.
• Solve problems that involve combinations with restrictions including specific objects grouped together and selection from multiple groups.
• Model and solve problems that involve permutations and combinations including probability problems, with and without technology.