Counting Outcomes — the Counting Principle (Grade 7)
To count the total ways two (or more) choices can combine, multiply the number of options at each stage — the fundamental counting principle. If you pick a shirt (3 options) and a hat (2 options), there are 3 × 2 = 6 outfits. A tree diagram shows every branch, and the counting principle gives the total without drawing them all.
Understanding counting outcomes — the counting principle
To count the total ways two (or more) choices can combine, multiply the number of options at each stage — the fundamental counting principle. If you pick a shirt (3 options) and a hat (2 options), there are 3 × 2 = 6 outfits. A tree diagram shows every branch, and the counting principle gives the total without drawing them all.
Key Idea
To count the total ways two (or more) choices can combine, multiply the number of options at each stage — the fundamental counting principle. If you pick a shirt (3 options) and a hat (2 options), there are 3 × 2 = 6 outfits. A tree diagram shows every branch, and the counting principle gives the total without drawing them all.
Seeing it in action
Worked example
3 shirts and 4 pants — how many outfits?
Multiply: 3 × 4 = 12 outfits.
3 choices × 4 choices = 12 total outcomes.
Try a few
2 breads × 3 fillings sandwiches?
Flip a coin and roll a die — total outcomes?
2 × 6.
5 entrées × 2 desserts?
Spinner
A calm probability game for reading spinner sectors, fractions, complements, and comparisons.
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