Favourable cases over possible cases

Observation — From the equiprobable space to combinatorics

When the sample space has equiprobable outcomes, probability becomes a problem of combinatorics: $P(E)=\frac{\#\,\text{favourable cases}}{\#\,\text{possible cases}}.$ The four formulae of combinatorics (permutations, arrangements, combinations, arrangements with repetition) apply very often: it is essential always to ask whether order matters and whether repetitions are allowed.

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Topics: Probability
Concepts: Combinatorics · Favourable cases over possible cases · Probability
Skills: Combinatorics · Probability calculation