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Counting & combinatorics
The bridge from foundations to probability.
How many passwords, poker hands, or committees are possible? Counting answers questions too big to list — and since probability is just 'favorable outcomes ÷ total outcomes', counting is the doorway into probability and statistics. This short course is a real bridge, not a footnote.
Your progress
4 lessons
The big ideas
Independent choices multiply
The fundamental counting principle: each independent stage multiplies the count, which is why possibilities explode and brute force fails.
Order is the deciding question
Permutations count ordered arrangements; combinations count unordered selections. Asking 'does rearranging make it different?' is half of correct counting.
Counting becomes probability
P(event) = favorable ÷ total — and both are counts. Combinations are literally the binomial distribution's coefficients.
The course — start at lesson one
- 01The counting principle & factorialsIndependent choices multiply; n! counts arrangements.Easy
- 02PermutationsOrdered selection, factorial growth, and why shuffles are unique.Easy
- 03CombinationsUnordered selection — divide out the orderings. Order matters or not?Easy
- 04Repetition, identical items & probabilityRepeats, identical-item arrangements, and the handoff to probability.Medium
Out in the world
Password & security strength
Attacker-years are computed straight from the counting principle: more characters multiply the possibilities.
Probability & gambling odds
Lottery and poker odds are pure combinations — the count is the consumer-warning label.
Sampling & distributions
How many samples could be drawn, and the shapes of distributions, are counting questions underlying all of statistics.
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