Permutation & Combination Calculator
Calculate permutations and combinations with step-by-step explanations and visualizations.
Calculator
Must be less than or equal to total items
Result
Visualization
Permutations
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Combinations
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Formulas & Explanation
Permutation Formula
Permutations calculate the number of ways to arrange ‘r’ items from a set of ‘n’ items where order matters.
Example: The number of ways to award 1st, 2nd, and 3rd place from 5 contestants.
Combination Formula
Combinations calculate the number of ways to choose ‘r’ items from a set of ‘n’ items where order does not matter.
Example: The number of ways to choose 3 team members from 5 available players.
Factorial Notation
n! (n factorial) is the product of all positive integers from 1 to n.
Example: 5! = 5 × 4 × 3 × 2 × 1 = 120
Practical Examples
Password Combinations
How many 4-digit PIN codes can you create with 10 numbers?
Answer: P(10, 4) = 5,040
Committee Selection
How many ways to choose 3 people from 10 for a committee?
Answer: C(10, 3) = 120
Race Outcomes
How many ways can 5 runners finish 1st, 2nd, and 3rd?
Answer: P(5, 3) = 60