Permutation and Combination Calculator
Permutation and Combination Calculator
The Permutation and Combination Calculator helps you find the number of possible arrangements and selections from a given set. It is widely used in probability, statistics, and combinatorics.
What are Permutations and Combinations?
Permutations and combinations are mathematical concepts used to count possible arrangements of objects from a set. They belong to combinatorics, a branch of mathematics dealing with counting and arrangements.
- Permutation: Order matters
- Combination: Order does not matter
Input Values
- Total items in set (n): 6
- Items selected (r): 2
Permutation Formula (nPr)
Permutation calculates arrangements where order is important.
nPr = n! / (n - r)!
Example: 6P2 = 6! / (6 - 2)! = 30
Combination Formula (nCr)
Combination calculates selections where order does not matter.
nCr = n! / (r! × (n - r)!)
Example: 6C2 = 6! / (2! × 4!) = 15
Difference Between Permutation and Combination
- Permutation: Order matters (arrangements)
- Combination: Order does not matter (selections)
- Permutation results are always equal or greater than combinations
Factorial Concept
Factorial (n!) is the product of all positive integers from 1 to n.
- 6! = 6 × 5 × 4 × 3 × 2 × 1
- Used in both permutation and combination formulas
Applications of Permutations and Combinations
- Probability and statistics problems
- Cryptography and security systems
- Lottery and game design
- Data analysis and machine learning
- Decision making and optimization
FAQs
What is permutation?
Permutation is the arrangement of objects where order matters.
What is combination?
Combination is the selection of objects where order does not matter.
What is the formula for nPr?
nPr = n! / (n - r)!
What is the formula for nCr?
nCr = n! / (r! × (n - r)!)
References
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