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Permutations and Combinations
Permutations count ordered selections; combinations count selections when order does not matter.
How it works
Permutations count ordered selections; combinations count selections when order does not matter. Name the quantities before calculating, keep each transformation logically equivalent, and check the result against the original conditions.
Worked example
Choose 2 students from 5.
- Order does not matter, so use a combination.
- Compute C(5,2)=5!/(2!3!).
- Simplify to 10.
There are 10 pairs.
Try it now
These questions come from the same validated skill generator used by the game.
Common mistakes
- Using a remembered formula without identifying what each symbol represents.
- Changing a value or condition during an intermediate step.
- Skipping the final substitution, estimate, or logical check.
Challenge
Compare the number of ordered and unordered selections of 3 from 7.
Questions learners ask
What is the key idea in permutations and combinations?
Permutations count ordered selections; combinations count selections when order does not matter.
How should I check an answer?
Substitute it into the original conditions, check units and signs, and decide whether its size is reasonable.