Section 2.6 Summary
In this chapter we developed techniques applicable to a wide variety of counting problems. One should be able to decide which technique to use by determining if order matters or not; if repetition is allowed or not; if the underlying set is a multi-set or not. Table 2.6.1 summarizes these considerations.
Keep in mind that the Sum Rule and Product Rule underpin all these formulas, and that there is often more than one solution to any given counting problem.
| Permutation (order matters) | Combination (order does not matter) | |
| no repetition | Proposition 2.2.5 | Proposition 2.2.16 |
| with repetition | Proposition 2.4.2 | Theorem 2.4.5 |
| multiset | Proposition 2.2.10 | – – – – – |