Counting Combinations — the Counting Principle (Grade 7)
To count how many ways independent choices combine, multiply the number of options at each stage. With 4 shirts and 3 pants, there are 4 × 3 = 12 outfits — one branch of a tree for each. This counting principle is the foundation of combinatorics.
Understanding counting combinations — the counting principle
To count how many ways independent choices combine, multiply the number of options at each stage. With 4 shirts and 3 pants, there are 4 × 3 = 12 outfits — one branch of a tree for each. This counting principle is the foundation of combinatorics.
Key Idea
To count how many ways independent choices combine, multiply the number of options at each stage. With 4 shirts and 3 pants, there are 4 × 3 = 12 outfits — one branch of a tree for each. This counting principle is the foundation of combinatorics.
Seeing it in action
Worked example
4 shirts and 3 pants — how many outfits?
Multiply: 4 × 3 = 12.
Independent choices multiply.
Try a few
2 appetizers × 3 mains
5 colors × 2 sizes
A 4-option breakfast and a 3-option drink
Two-Ring Outpost
A calm two-circle Venn diagram game for sorting sets and practicing AND/OR logic.
Ready for the interactive lab?
Practice counting combinations — the counting principle in Numeris with instant feedback.
Master it in the workbook.
The Logic & Counting workbook is currently in editorial review.
Coming SoonWant a printable set too?
Get the free Reasonwell sample pack while the math workbook line is coming soon.