Combinatorics, probability and statistics

Combinatorics

A:

  • 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

B:

  • Simplifying expressions with factorials and binomial coefficients
  • Combinatorial equations

C:

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

Probability

A:

  • Classical probability definition

B:

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

C:

  • Binomial distribution (Bernoulli scheme)
  • Conditional probability

Statistics

A:

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

B:

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

C:

  • Summary statistics
  • Correlation coefficient