Counting Principle
Multiply the number of options at each step.
Key idea
Multiply the number of options at each step.
In depth
If one choice can be made in m ways and another in n ways, together they can be made in m × n ways. It extends to any number of independent stages.
Worked example
3 shirts × 4 trousers × 2 shoes = 24 outfits.
Formula
Real-world uses
- Counting possible passwords, menu combinations or outfit choices
Common mistake
Adding the numbers when the choices happen together.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Counting Principle?
Multiply the number of options at each step. It is a topic at the intermediate level in Probability & Statistics.
What is the formula for Counting Principle?
The key formula is n₁ × n₂ × ….
Where is Counting Principle used in real life?
Real-world examples: Counting possible passwords, menu combinations or outfit choices.
What should I learn before Counting Principle?
Make sure you are comfortable with Tree Diagrams, the previous topic in Probability & Statistics.
What is a common mistake with Counting Principle?
Adding the numbers when the choices happen together.
How can I practise Counting Principle?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Counting Principle?
Move on to Permutations next.
Related intermediate topics in Probability & Statistics
- Collecting Data and Sampling – Surveys, experiments and random sampling.
- Bias in Sampling – Systematic errors that make samples unrepresentative.
- Histograms – Bars showing frequency of numerical intervals.
- Dot Plots and Stem-and-Leaf Plots – Show the shape of small datasets.
- Mean – The arithmetic average.
- Median – The middle value of an ordered list.