Lesson 3 of 11Article20 min
Counting & Combinatorics
Product rule, sum rule, and bijections turn word problems into calculations. Distinguish ordered vs unordered, and with vs without repetition.
Systematic enumeration
Product rule, sum rule, and bijections turn word problems into calculations. Distinguish ordered vs unordered, and with vs without repetition.
- Inclusion–exclusion corrects overcounting unions.
- Pigeonhole principle: n+1 pigeons, n holes → some hole has ≥2.
- Burnside (preview): count distinct objects under symmetry.
Worked example
Committees of 3 from 10 people: C(10,3)=120. If order (president/secretary/treasurer) matters: P(10,3)=720.