Permutation & Combination Calculator
Calculate nPr (Permutations) and nCr (Combinations) with detailed explanations
Enter Values
Total number of items available
Number of items to select
Result
Understanding Permutations & Combinations
Permutation (nPr)
Formula: P(n, r) = n! / (n - r)!
When to use: When the order of selection matters
Example: Selecting 3 winners (1st, 2nd, 3rd) from 10 contestants - order matters because positions are different
Combination (nCr)
Formula: C(n, r) = n! / (r! Γ (n - r)!)
When to use: When the order of selection doesn't matter
Example: Selecting 3 team members from 10 people - order doesn't matter because all members have equal roles
Key Points
- n must be greater than or equal to r (n β₯ r)
- Both n and r must be non-negative integers
- P(n, r) β₯ C(n, r) - Permutations are always greater than or equal to combinations
- Factorial (!) means: n! = n Γ (n-1) Γ (n-2) Γ ... Γ 2 Γ 1
- Special case: 0! = 1
Related combinatorics tools
Advertisement
π’ Advertisement Space
Responsive In-Content Ad Unit
Share this tool
Help someone else shortcut their work
Send this page to a friend, student, or teammate who could benefit from it.