Discrete Math › Section D · Counting › Topic D.2
The sum and product principles
Almost every counting argument is built from two moves: add when the outcomes split into separate cases, and multiply when an outcome is built in stages. Knowing exactly when each move is allowed is what keeps counts honest.
In this topic
- Counting without listing
- The sum principle
- The product principle
- Same number of choices, not the same choices
- Worked example: two styles of code
- Counting functions and subsets
- Counting the complement
- Worked example: when multiplying fails
- Common mistakes to avoid
- Key takeaways
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