doomath Calculator
Permutations & Combinations (nPr & nCr)
Compute combinations nCr, permutations nPr, factorials, permutations with repetition, and probability odds with step-by-step KaTeX reduction.
InputsChange a value to recalculate instantly
ResultUpdates as you type
FORMULA & STEPSPermutations & Combinations (nPr & nCr) — Mathematical Derivation & Steps
2 StepsSequential Calculation Breakdown
1
Validate n and r
0 ≤ r ≤ n, so both formulas apply.
2
Evaluate factorials
Use factorial products to evaluate the formulas.
λ DooMathWork with this calculation
Local · deterministic · optionalQuick mathNatural-language-style shortcuts for deterministic arithmetic.
Calculator guide
How to use the Permutations & Combinations (nPr & nCr)
Compute combinations nCr, permutations nPr, factorials, permutations with repetition, and probability odds with step-by-step KaTeX reduction.
01Set inputsChoose values, units and assumptions.
02Apply the modelnCr = n! / [r!(n - r)!]; nPr = n! / (n - r)!; Repetitions: n^r; Multiset: (n+r-1)! / [r!(n-1)!]
03Read the resultCheck the output against the assumptions before using it.
What this calculator does
Enter set size n and sample size r. The solver determines unordered selections (combinations) and ordered sequences (permutations).
Formula & method
nCr = n! / [r!(n - r)!]; nPr = n! / (n - r)!; Repetitions: n^r; Multiset: (n+r-1)! / [r!(n-1)!]
Assumptions & notes
- Combinations disregard order; permutations require specific ordering.
- nCr values form Pascal's Triangle rows.
- By mathematical definition, 0! = 1.