Grade 7 Skill Alignment: Related to CCSS 7.SP.C.8.b (organized lists and tree diagrams)
Counting Combinations — the Counting Principle (Grade 7)
To count how many ways independent choices combine, multiply the number of options at each stage.
What it is
Understanding counting combinations — the counting principle
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.
Worked Example
Seeing it in action
1
Worked example
4 shirts and 3 pants — how many outfits?
Multiply: 4 × 3 = 12.
Visual model
Independent choices multiply.
Watch for this
A common mistake, and the fix
Adding the choices instead of multiplying.
4 shirts and 3 pants are 4 + 3 = 7 pieces of clothing, but 4 × 3 = 12 outfits, because each shirt goes with each of the 3 pants. Drawing the first shirt’s 3 branches of a tree shows why.
Interactive Check
Try a few
2 appetizers × 3 mains
Answer: 6
5 colors × 2 sizes
Answer: 10
A 4-option breakfast and a 3-option drink
Answer: 12
Try it in Numeris.
A short lesson, then practice with feedback on every answer.
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