Overview
When selecting a subset of items, the number of outcomes depends on whether order matters. Permutations nPr count every distinct ordering, while combinations nCr count each subset once regardless of order. These counts are used in probability, draws and task assignments.
Formula
nPr = n! ÷ (n − r)!, and nCr = nPr ÷ r!.
How it works
Enter n
The total number of available items.
Enter r
The number of items selected, not exceeding n.
Decide whether order matters
Choose a permutation if order matters, otherwise a combination.
Read the result
nPr, nCr and the related factorials appear.
Worked examples
Example 1: choose 2 of 5 with order
5P2 = 5 × 4 = 20.
Example 2: choose 2 of 5 without order
5C2 = 20 ÷ 2 = 10.
Frequently asked questions
What is the difference between a permutation and a combination?
A permutation treats the order of selected items as important, while a combination counts the same group only once.
When does nPr equal nCr?
When r = 0 or r = 1, because ordering zero or one item does not change the count.
Does the calculator allow repetition?
No, it handles selection without repetition. For repetition, use nʳ for permutations or C(n + r − 1, r) for combinations.
This calculator is for educational and informational purposes only and is not a substitute for professional advice.