Permutation & Combination Calculator
Calculate nPr (permutations) and nCr (combinations)
Permutation
10P3
720
n!/(n-r)! = 10!/7!
Order matters
Combination
10C3
120
n!/[r!(n-r)!] = 10!/[3! × 7!]
Order does not matter
Examples
Pascal's Triangle (C(n,r))
1
1
1
1
2
1
1
3
3
1
1
4
6
4
1
1
5
10
10
5
1
1
6
15
20
15
6
1
1
7
21
35
35
21
7
1
1
8
28
56
70
56
28
8
1
1
9
36
84
126
126
84
36
9
1
1
10
45
120
210
252
210
120
45
10
1
Each number is the sum of the two numbers above it
Formulas
Without Repetition
Permutation:
nPr = n! / (n-r)!
Combination:
nCr = n! / [r! × (n-r)!]
With Repetition
Permutation:
n^r
Combination:
C(n+r-1, r)
Key Difference
- Permutation: Arrangement where order matters (ABC ≠ CBA)
- Combination: Selection where order does not matter (ABC = CBA)