Counting & Probability· Study notes
Discrete and Data
Discrete mathematics for problem solvers: counting principles, combinations, casework and complements, stars and bars, the binomial theorem, inclusion–exclusion, recursion, and probability through expected value.
What you'll be able to do
- Count arrangements and selections without double counting
- Prove combinatorial identities two ways
- Compute probabilities with conditioning and independence
- Use linearity of expectation
Read the notes as a guided lesson
Walk the notes one box at a time — prose, worked examples, quick checks — with a timed practice round after every section. For the full course with interactive lessons, go back to the course.
Every test ends with a score by topic and a list of what to revisit. Test out of a topic with 80% or better to mark it mastered.
Topics
Counting Strategies: Casework, Complementary & Overcounting
12 lessonsCompetition counting & probability, Unit 2
Distributions: Stars & Bars and Integer Solutions
12 lessonsCompetition counting & probability, Unit 3
Binomial Theorem, Pascal & Combinatorial Identities
12 lessonsCompetition counting & probability, Unit 4
Inclusion–Exclusion, Derangements & Pigeonhole
12 lessonsCompetition counting & probability, Unit 5
Recursion, Catalan Numbers & Generating Functions
12 lessonsCompetition counting & probability, Unit 6
Probability Fundamentals & Geometric Probability
12 lessonsCompetition counting & probability, Unit 7
Conditional Probability, Independence & Bayes
12 lessonsCompetition counting & probability, Unit 8
Expected Value, Linearity & Advanced Probability
12 lessonsCompetition counting & probability, Unit 9
Identities and Techniques, Proved
9 lessonsThe hockey stick, Vandermonde, absorption, stars and bars, inclusion–exclusion and linearity — each one proved, not just stated