Permutation & Combination Calculator

Advanced Mathematical Tool

Real-time calculations with detailed explanations

Permutation & Combination Calculator

Calculation Result

P(n, r) = n! / (n - r)!
P(5, 3) = 5! / (5 - 3)! = 120 / 2 = 60
60

Advanced Features

Calculation History

Track your previous calculations

Probability Mode

Calculate probability of events

List Generator

Generate all possible arrangements

Pascal's Triangle

Visualize combinations

Multiple Calculations

Compare different scenarios

Export Results

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Calculation History

Understanding Permutations and Combinations: A Complete Guide

What are Permutations and Combinations?

Permutations and combinations are fundamental concepts in mathematics that deal with counting and arranging objects. While they might seem similar, they serve different purposes in probability, statistics, and various real-world applications.

Permutations (nPr)

Permutations refer to the number of ways to arrange objects where order matters. For example, the arrangement ABC is different from BAC.

P(n, r) = n! / (n - r)!
Combinations (nCr)

Combinations refer to the number of ways to select objects where order doesn't matter. For example, ABC is the same as BAC.

C(n, r) = n! / [r! × (n - r)!]

How to Use This Calculator

Our permutation and combination calculator makes complex calculations simple. Follow these steps:

  1. Enter Values: Input the total number of items (n) and the number of items to select (r).
  2. Choose Calculation Type: Select between permutation (nPr) or combination (nCr).
  3. Set Options: Check "Allow repetition" if items can be selected more than once.
  4. Calculate: Click the calculate button to get instant results with step-by-step explanations.

Real-World Applications

Permutations and combinations have numerous practical applications:

  • Lotteries and Gambling: Calculating odds of winning
  • Computer Science: Algorithm design and cryptography
  • Genetics: Studying genetic combinations
  • Business: Optimizing team formations and project assignments
  • Sports: Tournament scheduling and player selection

Key Differences Between Permutations and Combinations

Aspect Permutations Combinations
Order Importance Order matters Order doesn't matter
Formula n! / (n - r)! n! / [r! × (n - r)!]
Example Arranging books on a shelf Selecting committee members
Result Larger number Smaller number