Using the Permutation and Combination Calculator
Choose n as the number of distinct available items and r as the number selected. This version selects without replacement, so r cannot exceed n.
Worked example
Use the example inputs below to reproduce this result. These are the form's starting values, not recommended targets. Changing your inputs updates your result above; this worked example stays fixed for comparison. Results are rounded for display.
Example inputs
- Number of items
- 10
- Number selected
- 3
Example result
- Permutations
- 720
- Combinations
- 120
Method and assumptions
Permutations = n!/(n−r)!; combinations = n!/[r!(n−r)!].
Define the event before calculating
A probability or count depends on what qualifies as an outcome. Decide whether order matters, whether items can repeat and whether events are independent before choosing inputs. Two questions using the same numbers can have different answers when these assumptions differ. Express a probability consistently as a fraction, decimal or percentage when comparing results.
Common question
Why are there more permutations than combinations?
Each unordered selection can be arranged in several orders. Permutations count all those arrangements separately, while combinations count the selected group once.
Guide updated .