BESTUTILS

Permutation & Combination Calculator

Calculate nPr, nCr, and factorials for probability and statistics

Permutation Calculator

nPr = n! / (n-r)!

About Permutations & Combinations

Permutations and combinations are fundamental concepts in probability and statistics used to count arrangements and selections.

How to Use:

  1. Choose between Permutation or Combination
  2. Enter the total number of items (n)
  3. Enter the number of items to choose (r)
  4. Click "Calculate" to see the result
  5. Use "Calculate n!" for factorial only

Key Differences:

Permutation (nPr):

Order matters. Used when arranging items where sequence is important.

Combination (nCr):

Order doesn't matter. Used when selecting items where sequence is irrelevant.

💡 Remember:

Permutations are always greater than or equal to combinations for the same n and r values!

Examples & Applications

Permutation Examples:

  • Password arrangements: 4 different letters from 26 = 26P4
  • Race positions: Top 3 finishers from 10 runners = 10P3
  • Seating arrangements: 5 people in 5 chairs = 5P5 = 5!
  • License plates: 3 letters from 26 = 26P3

Combination Examples:

  • Team selection: Choose 5 players from 12 = 12C5
  • Pizza toppings: Choose 3 from 10 toppings = 10C3
  • Committee formation: 4 members from 15 people = 15C4
  • Lottery numbers: Pick 6 from 49 numbers = 49C6

Quick Reference Formulas:

Factorial
n! = n × (n-1) × ... × 1
Permutation
nPr = n! / (n-r)!
Combination
nCr = n! / (r! × (n-r)!)