Counting, permutations, combinations, and core probability laws.
Number of ordered arrangements of r items from n.
Number of unordered selections of r items from n.
Product of all positive integers up to n.
Ordered arrangements of r items from n when repetition is allowed.
Arrangements of n items where some are identical.
Probability of an event with equally likely outcomes.
Probability that an event does not occur.
Probability that A or B occurs.
Probability of both independent events occurring.
Probability of A given that B has occurred.
Reverses conditional probabilities using prior knowledge.
Long-run average value of a random variable.
Measures the spread of a random variable around its mean.
Probability of k successes in n independent trials.
Probability of k events in a fixed interval given average rate λ.
Probability that the first success occurs on trial k.
Bell-curve probability density function.
Ratio of the probability of an event to its non-occurrence.
If n items go into k containers, some container holds at least this many.
Counts the union of overlapping sets without double counting.
Counts many recursive structures such as balanced parentheses.
Ways to distribute n identical items into k distinct groups.