Permutation & Combination Calculator
Calculate permutations, combinations, and factorial values with detailed explanations. Perfect for students, researchers, and professionals working with combinatorial mathematics.
Permutation & Combination Calculator
Calculate permutations, combinations, and factorial values with detailed explanations
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About Permutations & Combinations
• Combination: Order doesn't matter (C(n,r))
• Permutation: Order matters (P(n,r))
• Factorial: n! = n × (n-1) × (n-2) × ... × 1
• Rule: r must be ≤ n
Common Examples
Understanding Permutations & Combinations
Permutations and combinations are fundamental concepts in combinatorial mathematics that help us count the number of possible arrangements or selections from a set of items.
Combinations (C(n,r)) count how many ways we can choose r items from n items when the order doesn't matter. This is useful for scenarios like selecting committee members or choosing lottery numbers.
Permutations (P(n,r)) count how many ways we can arrange r items from n items when the order does matter. This applies to situations like arranging books on a shelf or ordering participants in a race.
How to Use This Calculator
When to Use Each Type
Use Combinations When:
Order doesn't matter: choosing team members, lottery numbers, committee selections, card hands, or any selection where arrangement isn't important.
Use Permutations When:
Order matters: arranging books, ranking competitors, creating passwords, seating arrangements, or any scenario where the sequence is important.