Combinatorics, Probability & Statistics One continuous course in three acts: first learn to COUNT (combinatorics), then use counting to measure CHANCE (probability), then use chance to read DATA honestly (statistics). Each act powers the next — taught from zero, no prior experience assumed.
Take the placement test
A quick adaptive test finds your level, seeds your rating, and shows where to start in this course.
The course — 12 units, in order
01 Counting Principles The multiplication and addition principles, complementary counting, and organized lists — how to count without counting. Start 02 Permutations & Arrangements Factorials, arrangements of all or some objects, repeated letters, and seating with restrictions. Start 03 Combinations Choosing without order: nCr, committees, at-least and at-most counts, and when order matters vs when it doesn't. Start 04 Pascal's Triangle & the Binomial Theorem The triangle that counts everything: binomial coefficients, expanding powers, and finding specific terms. Start 05 Probability Models Sample spaces, events, equally-likely outcomes, complements, and the addition rule with Venn diagrams. Start 06 Conditional Probability & Independence How information changes chance: P(A|B), the multiplication rule, independence, weighted trees, and Bayes by table. Start 07 Random Variables & Expected Value Turning outcomes into numbers: probability distributions, expected value, variance, and what makes a game fair. Start 08 The Binomial Distribution Repeated independent trials: binomial probabilities, expected count np, shape, and simulation. Start 09 Describing Data Center and spread done right: mean, median, IQR, standard deviation, boxplots, and the 1.5×IQR outlier fence. Start 10 Distribution Shape & Position Histograms and shape, percentiles, z-scores, and the normal curve with the 68–95–99.7 rule. Start 11 Two-Variable Data Scatterplots, the correlation coefficient, the least-squares line, and why correlation is not causation. Start 12 Sampling, Studies & Inference Random sampling, bias, experiments vs observation, simulation-based inference, and margin of error — the capstone. Start