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Permutations & combinations formulas
11 formulas for Permutations & combinations, from the Algebra section of the Quantix formula library. Tap 🧮 next to a formula to solve it for any variable with step-by-step working.
| Name | Formula | Note |
|---|---|---|
| Factorial | n! = n(n − 1)(n − 2)…1; 0! = 1 | |
| Permutations | ⁿPᵣ = n! / (n − r)! | |
| Combinations | ⁿCᵣ = n! / [r!(n − r)!] | |
| Symmetry | ⁿCᵣ = ⁿCₙ₋ᵣ | |
| Pascal's rule | ⁿCᵣ + ⁿCᵣ₋₁ = ⁿ⁺¹Cᵣ | |
| Relation | ⁿPᵣ = r! · ⁿCᵣ | |
| Circular permutations | (n − 1)!; necklace (n − 1)!/2 | |
| Identical objects | n! / (p! q! r!) | |
| Distributing n identical items into r groups | ⁿ⁺ʳ⁻¹Cᵣ₋₁ | |
| Derangements | Dₙ = n! [1 − 1/1! + 1/2! − … + (−1)ⁿ/n!] | |
| Number of diagonals of n-gon | n(n − 3) / 2 |
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