Combinations
Unordered selections.
Key idea
Unordered selections.
In depth
A combination is an unordered selection: C(n, r) = n!/(r!(n − r)!). Dividing the permutation count by r! removes the repeated orderings of the same group.
Worked example
Choosing 3 of 10 for a committee: C(10, 3) = 120.
Formula
Real-world uses
- Choosing a committee or a lottery ticket where order does not matter
Common mistake
Using permutations and over-counting.
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 Combinations?
Unordered selections. It is a topic at the advanced level in Probability & Statistics.
What is the formula for Combinations?
The key formula is C(n,r) = n!/(r!(n−r)!).
Where is Combinations used in real life?
Real-world examples: Choosing a committee or a lottery ticket where order does not matter.
What should I learn before Combinations?
Make sure you are comfortable with Permutations, the previous topic in Probability & Statistics.
What is a common mistake with Combinations?
Using permutations and over-counting.
How can I practise Combinations?
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 Combinations?
Move on to Addition Rule 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.