Permutation & Combination Calculator

Calculate permutations (nPr) and combinations (nCr) for any values of n and r with detailed explanations.

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Results
Enter values for n and r to see results
How It Works

Permutations (nPr)

Permutations count the number of ways to arrange r items from n total items where order matters.

Formula: nPr = n! / (n-r)!

Example: Arranging 3 people from 5 people in a line = 5P3 = 60 ways

Combinations (nCr)

Combinations count the number of ways to choose r items from n total items where order doesn't matter.

Formula: nCr = n! / (r! × (n-r)!)

Example: Choosing 3 people from 5 people for a team = 5C3 = 10 ways

Common Examples

When to Use Permutations:

  • • Arranging people in a line
  • • Password combinations with order
  • • Race finishing positions
  • • Seating arrangements

When to Use Combinations:

  • • Selecting team members
  • • Choosing lottery numbers
  • • Selecting committee members
  • • Choosing pizza toppings