Permutation & Combination Calculator
Calculate permutations, combinations, and factorials. Solve counting problems.
Visualization
Result
5C3
10
Formula: 5! / (3!(5-3)!)
Permutation (5P3):60
Combination (5C3):10
Ratio (P/C = r!):6
Counting Formulas
Permutation (no repetition)
nPr = n! / (n-r)!
Ordered arrangements of r items from n items
Permutation (with repetition)
n^r
Ordered arrangements allowing repetition
Combination (no repetition)
nCr = n! / (r!(n-r)!)
Unordered selections of r items from n items
Combination (with repetition)
(n+r-1)Cr
Unordered selections allowing repetition
Factorial
n! = n × (n-1) × ... × 2 × 1
Product of all positive integers up to n

Key Relationships

nPr = nCr × r!
nCr = nC(n-r)
nC0 + nC1 + ... + nCn = 2^n

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