Permutations
Ordered arrangements.
Key idea
Ordered arrangements.
In depth
A permutation is an ordered arrangement. The number of ways to arrange r items from n is P(n, r) = n!/(n − r)!. Order matters, so ABC and CBA differ.
Worked example
Awarding gold, silver, bronze among 10 runners: 10 × 9 × 8 = 720.
Formula
Real-world uses
- Arranging runners in a race order or seating guests at a table
Common mistake
Using it when order does not matter.
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 Permutations?
Ordered arrangements. It is a topic at the advanced level in Probability & Statistics.
What is the formula for Permutations?
The key formula is P(n,r) = n!/(n−r)!.
Where is Permutations used in real life?
Real-world examples: Arranging runners in a race order or seating guests at a table.
What should I learn before Permutations?
Make sure you are comfortable with Counting Principle, the previous topic in Probability & Statistics.
What is a common mistake with Permutations?
Using it when order does not matter.
How can I practise Permutations?
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 Permutations?
Move on to Combinations next.
Related advanced topics in Probability & Statistics
- Quartiles and IQR – Quartiles split data into four parts; IQR = Q3 − Q1.
- Box Plots – Five-number summary visualised.
- Outliers – Values beyond 1.5 IQR from the quartiles.
- Variance – Average squared deviation from the mean.
- Standard Deviation – Square root of variance; typical spread.
- Sample vs Population Variance – Divide by n−1 for sample variance.