Combinations & Permutations Calculator

Calculate nCr (combinations) and nPr (permutations) with detailed factorial breakdown and step-by-step solutions.

nCr & nPr Calculator

Enter n and r to compute

n (Total Items)

Total number of items

r (Chosen Items)

Number to choose

Combinations (nCr)

Order doesn't matter

Permutations (nPr)

Order matters

Enter values for n and r, then tap Calculate.

Step-by-step Solution

Pascal's Triangle (First 8 Rows)

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

Each number is nCr where n = row, r = position

Key Formulas

nCr = n! / (r! × (n−r)!)

nPr = n! / (n−r)!

n! = n × (n−1) × ... × 2 × 1

Combinations: order doesn't matter (teams)
Permutations: order matters (rankings)

Related Calculators

When to Use

Combinations (nCr): selecting a team, lottery numbers

Permutations (nPr): podium rankings, passwords