Permutation and Combination Calculator
Calculate permutations (nPr) and combinations (nCr) with detailed step-by-step solutions and factorial calculations
Calculator
Check if the same item can be selected multiple times
Formulas & Concepts
Permutation Formula
P(n,r) =
n!
(n-r)!
Order matters
Combination Formula
C(n,r) =
n!
r! × (n-r)!
Order doesn't matter
With Repetition
P(n,r) = n^r(permutations)
C(n,r) = C(n+r-1,r)(combinations)
Key Relationships
P(n,r) = C(n,r) × r!
C(n,r) = C(n,n-r)
P(n,n) = n!
C(n,0) = C(n,n) = 1
Common Examples
Permutation:
Race positions, passwords, arrangements
Combination:
Team selection, lottery numbers, committees
Frequently Asked Questions
Permutations count arrangements where order matters (like race positions: 1st, 2nd, 3rd are different). Combinations count selections where order doesn't matter (like choosing team members: selecting A,B,C is the same as C,A,B). Permutations are always ≥ combinations for the same n and r.
Tips
- Enter the dimensions in the same unit for consistency.
- Results update automatically as you type.
- Use the unit selector to convert between different measurement systems.