Probability
Counting Outcomes – Applying the Counting Principle
With the Fundamental Counting Principle in hand, you can now count the total number of outcomes for any real multi-step scenario – outfits assembled from separate wardrobe categories, meal deals built from separate menu categories, or any situation built from several independent choices made one after another.
The key skill here is recognising the separate stages in a word problem and identifying how many options each stage has, before multiplying. Once the stages are identified correctly, the calculation itself is simple.
Counting Real-World Outcomes
Identify each independent stage of choice in the scenario, count the options at each stage, then multiply them all together.
A wardrobe has 4 shirts, 3 pairs of pants, and 2 pairs of shoes. How many complete outfits are possible?
4 × 3 × 2 = 24 outfits.
Real-Life Application
- Restaurant menus: counting every possible combo meal from separate menu sections.
- Car customisation: counting every possible configuration of engine, colour, and interior trim.
- Event planning: counting possible combinations of venue, date, and catering option.
Key Takeaways
- Real-world counting problems involve identifying separate, independent stages.
- Multiply the number of options at each stage to find the total outcomes.
- Correctly identifying the stages is the most important step.
Practice: Counting Outcomes
Counting Outcomes