Permutation and Combination Calculator
Permutation and Combination Calculator
Permutations and Combinations Explained
In mathematics, permutations and combinations are two different ways of grouping items from a larger set. Both are fundamental concepts in combinatorics and probability. The essential difference between them is whether the order of the selected items matters.
Key Differences
Understanding when to use a permutation versus a combination is the most important step. This table breaks down the main distinctions.
| Feature | Permutation | Combination |
|---|---|---|
| Order | The order of the items matters. (e.g., "1, 2, 3" is different from "3, 2, 1") | The order of the items does not matter. (e.g., "1, 2, 3" is the same as "3, 2, 1") |
| Example | Choosing the first, second, and third place winners in a race. | Choosing a team of three people from a group. |
| Formula | nPr = n! / (n - r)! | nCr = n! / (r! * (n - r)!) |
How to Use This Calculator
- Select whether you want to calculate a Permutation (nPr) or a Combination (nCr).
- Enter the total number of items in the set (n).
- Enter the number of items you want to choose from that set (r).
- The calculator will automatically show the total number of possible arrangements or groups.
Note: The calculations involve factorials (n!), which grow extremely quickly. This calculator supports inputs for 'n' up to 170. Any value higher than that will result in a number too large for standard calculations.