Combination Calculator
Calculate combinations (nCr) and permutations (nPr) for counting and probability problems.
Input Values
n = total number of items
r = number of items to select
Formulas
Combination (order doesn't matter)
C(n,r) = n! / (r!(n-r)!)
Permutation (order matters)
P(n,r) = n! / (n-r)!
Combination with Repetition
C(n+r-1, r)
Permutation with Repetition
n^r
Quick Examples
C(5,2) - Choose 2 from 510
C(10,3) - Choose 3 from 10120
C(52,5) - Poker hand2,598,960
Combinations C(10,3)
120
ways to choose 3 from 10
CC(10,3)
120
PP(10,3)
720
n!10!
3,628,800
r!3!
6
All Counting Results
Combination (no repetition)120
Permutation (no repetition)720
Combination (with repetition)220
Permutation (with repetition)1,000
Step-by-Step Calculation
C(10,3) = 10! / (3! x (10-3)!)
= 10! / (3! x 7!)
= 120
Combinations vs Permutations
Combinations
Order does NOT matter. Used when selecting a group.
Example: Choosing 3 people for a committee from 10 people.
Permutations
Order DOES matter. Used when arranging items.
Example: Arranging 3 books on a shelf from 10 books.