The decision rule
| Question | Use |
|---|---|
| Does order matter? | nPr(n,r) |
| Does order not matter? | nCr(n,r) |
Combination example
Choose 3 students from a group of 12 for one committee.
nCr(12,3) = 220
The order of the three names does not create a new committee.
Permutation example
Award first, second and third place among 12 students.
nPr(12,3) = 1320
Changing the order changes the outcome.
Factorial connection
nCr = n! / (r!(n-r)!) nPr = n! / (n-r)!
- Identify n, the total number of available items.
- Identify r, the number selected or arranged.
- Decide whether order matters.
- Enter
nCr(n,r)ornPr(n,r).
Practice
How many 4-person groups can be formed from 10 people?
Show answer
nCr(10,4) = 210.
Try the method now
Open the calculator in a separate tab and reproduce the worked example.
Related guides
Reviewed July 17, 2026.