Discrete Math › Section D · Counting › Topic D.8
Advanced counting: derangements and functions
Some counts are hard to make directly but easy to make by subtracting what you do not want. Inclusion-exclusion in its full form handles three classic problems: distributions with upper limits, derangements, and functions that hit every target.
In this topic
- Counting what goes wrong
- Inclusion-exclusion in full
- Worked example: upper limits on a distribution
- Derangements
- Worked example: the gift-exchange draw
- The surprising limit
- Counting onto functions
- Worked example: no idle workers
- Common mistakes to avoid
- Key takeaways
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