Addition vs Multiplication
Disjoint alternatives combine by addition, while sequential choices combine by multiplication when each branch's continuations are counted correctly.
What you'll learn
- Distinguish separate alternatives from stages that every final outcome must complete.
- Explain multiplication using 'for each first choice' language and a complete outcome grid.
- Check disjointness and branch sizes before adding or multiplying counts.
Before you start
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Worked recap: Add alternatives; multiply stages
Choosing one of 2 shirts and then one of 3 pairs of pants creates 2 × 3 = 6 outfits. Each shirt has three continuations.
If instead you choose one item from 2 shirts or 3 pairs of pants, the alternatives are disjoint: there are 2 + 3 = 5 choices. Check what one completed outcome contains before deciding how to count.