When should you use a permutation or combination?
Method: Use a permutation when changing the order creates a different outcome. Use a combination when the selected group is the same regardless of order.
Decide whether a swap creates a new outcome
- Define one outcome in words.
- Swap the order of two selected items.
- If the outcome changes, use permutations.
- If it stays the same group, use combinations.
Compare a committee with assigned roles
Choosing three finalists from ten is a combination. Awarding gold, silver, and bronze to three of ten is a permutation because each position has a different meaning.
Know what this counting model assumes
Define the outcome before choosing the formula
A race podium, password, and seating plan are ordered. A committee or selected sample is normally unordered. The same objects can therefore produce different counts depending on the question. Write one outcome in words and swap two positions. The answer to whether anything changed determines the model more reliably than memorizing notation.
The displayed difference between permutations and combinations equals the number of internal orders for the selected group. That multiplier helps detect accidental double-counting when a hand calculation lists the same group several ways.
Boundary of the result
This calculator assumes selection without replacement and treats the available objects as distinct.
Continue with the method
Use the permutations versus combinations and the probability guide and the expected value calculator with three outcomes to move from a quick result to a complete reasoning process.