Calculator
Combination & Permutation Calculator
Calculate nPr and nCr with step-by-step solutions, repetition variants, and Pascal's triangle.
🔢Input
📐Formulas
Permutation (no repetition)
nPr = n! / (n−r)!
Combination (no repetition)
nCr = n! / (r! × (n−r)!)
Permutation (with repetition)
nʳ
Combination (with repetition)
C(n+r−1, r) = (n+r−1)! / (r! × (n−1)!)
📊Results
nPr
60
nCr
10
Perm w/ Rep (nʳ)
125
Comb w/ Rep
35
📝Step-by-Step
Permutation P(5, 3):
P(5, 3) = 5! / (5-3)!
= 5! / 2!
= 5 × 4 × 3 × 2 × 1 / 2 × 1
= 5 × 4 × 3
= 60
Combination C(5, 3):
C(5, 3) = 5! / (3! × (5-3)!)
= 5! / (3! × 2!)
= 5 × 4 × 3 × 2 × 1 / (3 × 2 × 1 × 2 × 1)
= 10
🔺Pascal's Triangle (Rows 0–8)
1
11
121
1331
14641
15101051
1615201561
172135352171
18285670562881