Combinatorics, probability and statistics

The topic is divided into the following subtopics:

Combinatorics
Probability
Statistics

Combinatorics

Part I:

Combinatorial product rule and sum rule
Arrangements without repetition / k-permutations without repetition
Arrangements with repetition / k-permutations with repetition
Permutations without repetition
Permutations with repetition
Selections without repetition / k-combinations without repetition

Part II:

Simplifying expressions with factorials and binomial coefficients
Combinatorial equations

Part III:

Selections with repetition/ k-combinations with repetition
Combinatorial inequalities
Binomial theorem

Probability

Part I:

Classical probability definition

Part II:

Geometrical probability
Probability of complementary event
Probability of union of events
Probability of intersection of independent events

Part III:

Binomial distribution (Bernoulli scheme)
Conditional probability

Statistics

Part I:

Measures of location (mean, median, mode)
Arithmetic, geometric and harmonic mean

Part II:

Measures of variability (variance, standard deviation, coefficient of variation)

Part III:

Summary statistics
Correlation coefficient