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The Counting Principle

When decisions happen one after another, the number of outcomes is the product of the number of options at each stage. A decision tree shows why: every stage multiplies the leaves.

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How many outfits can you make from 3 shirts, 2 pairs of pants and 2 pairs of shoes? Instead of listing them, build a decision tree: one level per decision, one branch per option. The root is the moment before any choice.

\text{no decisions yet: } 1 \text{ outcome}

Each factor is coloured like its stage in the tree. A bracketed sum is an either-or stage: its groups add, and the result multiplies with everything else.

The Counting Principle

When decisions happen one after another, the number of outcomes is the product of the number of options at each stage. A decision tree shows why: every stage multiplies the leaves.

Step 1 of 18

Speed

\text{no decisions yet: } 1 \text{ outcome}

Each factor is coloured like its stage in the tree. A bracketed sum is an either-or stage: its groups add, and the result multiplies with everything else.

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The Counting Principle

See also

The Counting Principle

See also