There is an extremely powerful mnemonic scheme for never mixing up the combinatorial formulae: the problem of the slips. Every combinatorics problem can be recast as asking to draw objects from an urn of objects, and then answering two questions:
- are the slips numbered (each object is distinguishable) or blank (each object is identical to the others)?
- can the same object be drawn more than once (with replacement) or at most once (without replacement)?
The four combinations of these answers produce the four fundamental formulae of combinatorics. Reducing the statement of a problem to these two questions is almost always the decisive step.
Links
Topics: Combinatorics
Concepts: Combinatorial calculus · Combinations · Arrangements · Permutations
Methods: Slips table
Skills: Combinatorial calculus · Modelling