Counting Selections – Applying Combinations
With the combination formula established, you can now count the number of possible selections in real scenarios – forming a committee from a larger group, choosing which items to buy from a range, or picking a subset of anything where the order of picking doesn't matter.
The key skill, just like with counting outcomes earlier, is recognising when a word problem describes an unordered selection rather than an ordered arrangement – the word “choose” or “select” is often a strong clue that combinations, not permutations, are needed.
Applying Combinations to Selections
When a problem asks you to choose or select a group where order doesn't matter, use nCr with n as the total pool and r as the number selected.
A club has 8 members. How many different 3-person committees can be formed?
8C3 = 8! ÷ (3! × 5!) = 56.
Real-Life Application
- Jury selection: counting possible juries from a larger jury pool.
- Sports team selection: counting possible starting lineups from a squad.
- Survey sampling: counting possible samples chosen from a larger population.
Key Takeaways
- Selection problems where order doesn't matter use the combination formula.
- Words like “choose” or “select” are common clues for combinations.
- This is the same nCr formula applied to real-world group-selection scenarios.
Practice: Counting Selections
Counting Selections
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