Combinatorics: Counting Principles, Permutations, Combinations & Probability
Multiplication principle, FACT, PERMUT, COMBIN, multinomials, inclusion–exclusion, stars and bars, Pascal's triangle and the birthday problem: 8 graded labs on passwords, teams, menus and lottery odds.
The first lesson is free — no account needed.
About this course
A combinatorics course that turns counting problems into formulas you can check, on the kit room, lockers, passwords and raffle of one fictional sports club, for students, teachers and anyone preparing for a quantitative test. You count outfits, codes and menus with the multiplication principle, line-ups, round-table seatings and passwords with FACT and PERMUT, committees, quotas and toppings with COMBIN and COMBINA, flag orders, job teams and grid routes with the multinomial coefficient, overlapping members with two- and three-set inclusion-exclusion, voucher shares with stars and bars and an upper limit, Pascal's triangle and a binomial probability, and finish with the birthday problem for groups of 5 to 70 and the jackpot odds of a 6-from-49 lotto. The first lab is free.
Lessons
- The Multiplication Principle: Outfits, Codes & MenusFree
- Permutations: FACT, PERMUT & Repetition Pro
- Combinations: COMBIN, COMBINA & Subsets Pro
- Arrangements with Identical Items: the Multinomial Pro
- Inclusion–Exclusion: Counting Overlaps Pro
- Stars and Bars: Distributing Identical Items Pro
- Binomial Coefficients, Pascal's Triangle & Binomial Probability Pro
- The Birthday Problem & Lottery Odds Pro