SEC2_GYM · Probability · PROB.COMBINATORICS

Combinatorics

Intuition

Understand first, compress later.

Probability quantifies uncertainty. A good model starts with clear possible outcomes and conditions.

Switch representations

Sample spacesum of two dice

favourable outcomesremaining outcomes

All 36 pairs are equally likely, because both dice are fair. 6 of them satisfy the event — count the highlighted cells and divide by the total number of cells.

Formal view

You can combinatorics when you can recognise the underlying objects, select valid rules and check each step for equivalence or logical implication.

Why does it work?

This skill sits on a prerequisite network. If a step is unstable, repair the missing prerequisite instead of merely doing more items of the same type.