Permutation & Combination Calculator
Calculate permutations (nPr) and combinations (nCr) instantly with our free online tool. Perfect for probability, statistics, and combinatorics problems.
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Concepts & Formulas
What are Permutations?
Permutations (nPr) represent the number of ways to arrange ‘r’ items from a set of ‘n’ items where order matters.
Example: Arranging 3 books out of 5 on a shelf. The order matters.
What are Combinations?
Combinations (nCr) represent the number of ways to choose ‘r’ items from a set of ‘n’ items where order does not matter.
Example: Selecting 3 team members out of 5 candidates. Order doesn’t matter.
Practical Examples
Understanding Permutations and Combinations
Permutations and combinations are fundamental concepts in combinatorics and probability. They help us calculate the number of possible arrangements or selections in various scenarios.
When to Use Permutations
Use permutations when the order or arrangement matters. Examples include:
- Password combinations where sequence is important
- Race results with podium positions
- Scheduling a sequence of tasks
- Seating arrangements at a table
When to Use Combinations
Use combinations when the order does not matter, only the selection. Examples include:
- Selecting team members for a project
- Choosing lottery numbers (in most formats)
- Selecting ingredients for a salad
- Forming committees or groups
Key Differences
The fundamental difference between permutations and combinations is whether order matters. Permutations consider arrangements while combinations consider selections.
For the same values of n and r, the number of permutations is always greater than or equal to the number of combinations, since permutations account for different orderings of the same items.