Combinations Calculator

Combinations Calculator

Calculate combinations, permutations, and factorial values with visual analysis

🎯 Combinations Calculator

Calculate C(n,r) - choosing r items from n items without regard to order

C(n,r) = n! / (r! × (n-r)!)

📊 Results

Combination calculation results

Enter values to calculate combinations

🔄 Permutations Calculator

Calculate P(n,r) - choosing r items from n items where order matters

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

📊 Results

Permutation calculation results

Enter values to calculate permutations

📈 Factorial Calculator

Calculate n! - the product of all positive integers up to n

n! = n × (n-1) × (n-2) × ... × 2 × 1

📊 Results

Factorial calculation results

Enter a value to calculate factorial

📈 Growth Comparison

Visual comparison of combinations, permutations, and factorials

🌐 3D Mathematical Visualization

Interactive 3D representation of mathematical relationships

Use mouse to rotate and zoom

🔢 Mathematical Examples

Common combination and permutation scenarios

Combinatorics Guide

Understanding combinations, permutations, and factorials in mathematics

Combinatorics deals with counting, arrangement, and selection of objects. Combinations count selections where order doesn't matter, permutations count arrangements where order matters, and factorials represent the total arrangements of all items. These concepts are fundamental in probability, statistics, and discrete mathematics.

Combinations

Selecting items where order doesn't matter - like choosing team members

Permutations

Arranging items where order matters - like race finishing positions

Factorials

Total arrangements of all items - grows very rapidly with input size

Applications

Used in probability, statistics, cryptography, and algorithm analysis

Key relationships: C(n,r) = P(n,r) / r! and P(n,r) = n! / (n-r)!. Combinations are always less than or equal to permutations for the same values, since permutations account for different orderings of the same selection.

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