Business Mathematics and Statistics · Ch 2 — Algebra (Partial Fractions, Permutations, Combinations, Mathematical Induction, Binomial Theorem)
Combinations — Choosing Between Permutation and Combination, and Business Applications
Combinations — Choosing Between Permutation and Combination, and Business Applications
The single most useful question when solving a counting problem is: does the order of selection matter?
- If yes — the objects are being arranged, ranked, or assigned distinct roles — use a permutation.
- If no — the objects are simply being chosen or grouped with no distinction of order — use a combination.
| Situation | Order matters? | Use |
|---|---|---|
| Choosing 4 members for a committee | No | |
| Electing a chairman, secretary and treasurer from a group | Yes (3 distinct roles) | |
| Selecting 3 products to feature in an advertisement, all shown equally | No | |
| Ranking the top 3 salespersons out of 10 | Yes (1st, 2nd, 3rd differ) |
Combined selection-and-arrangement problems. Many real problems need both ideas in sequence: first select a group (combination), then arrange or assign roles within that group (permutation). For example, selecting a 5-member project team from 12 employees, and then separately deciding who among those 5 will be team leader, is a combination (choosing the 5) followed by choosing 1 leader from the 5 ( ways). …
The deciding question for any counting problem: if rearranging the chosen objects produces a genuinely different outcome, use a permutation; if it d …
A problem solved in two stages — a combination to choose a group, followed by a permutation (or further combinations) to arrange or assign roles within the chosen group — with the two …