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Combinations
A combination counts the unordered selections of r items chosen from n, using nCr = n! divided by r! times (n minus r)!.
What You'll Learn
A combination counts unordered selections of r items chosen from n.
The formula is nCr = n! divided by r! times (n minus r) factorial.
Example: 4C2 = 4!/(2! times 2!) = 24/4 = 6 unordered selections.
A combination is the permutation formula divided by r!, since order no longer matters.
If order matters, use a permutation instead of a combination.
What You'll Practice
1
Forming five-card hands with specific color or face card requirements
2
Committee selection problems with constraints on boys and girls
3
Geometric problems: counting triangles, line segments, and diagonals in polygons
4
At least/at most problems using case addition or complement method
Why This Matters
Combinations help you count choices when order doesn't matteressential for probability, statistics, and real-world decision-making. Whether you're analyzing card games, forming teams, or solving contest math problems, mastering combinations gives you the tools to calculate possibilities efficiently.
Before You Start — Make Sure You Can:
This Unit Includes
17 Video lessons
Practice exercises
Learning resources
Skills
Combinations
nCr Formula
Counting Principles
Complement Method
At Least/At Most
Card Problems
Selection Without Order
OH Curriculum Aligned