Calculate permutations (nPr) and combinations (nCr) with accurate results and detailed explanations.
Permutations and combinations are fundamental concepts in combinatorics that deal with arranging and selecting items from a set.
Permutations refer to the number of ways to arrange items where order matters.
| Type | Formula | Description |
|---|---|---|
| Permutation without repetition | nPr = n! / (n - r)! | Selecting r items from n without repetition where order matters |
| Permutation with repetition | nPr = n^r | Selecting r items from n with repetition allowed where order matters |
Combinations refer to the number of ways to select items where order does not matter.
| Type | Formula | Description |
|---|---|---|
| Combination without repetition | nCr = n! / (r! × (n - r)!) | Selecting r items from n without repetition where order doesn't matter |
| Combination with repetition | nCr = (n + r - 1)! / (r! × (n - 1)!) | Selecting r items from n with repetition allowed where order doesn't matter |