Permutation and Combination Calculator
Calculate permutations (order matters) and combinations (order does not matter) for any total items (n) and sample size (r).
Permutation nPr
720
n! / (n-r)!
Combination nCr
120
n! / (r! × (n-r)!)
nPr = n! / (n-r)!
nCr = n! / (r! x (n-r)!)
How to Use the Permutation and Combination Calculator
- Enter the total number of items in the set (n).
- Enter the number of items to select (r), where r ≤ n.
- View the calculated Permutations (nPr) and Combinations (nCr) instantly.
Formulas & Principles
Factorial: n! = n × (n - 1) × ... × 1 (with 0! = 1)
Permutation: nPr = n! / (n - r)!
Combination: nCr = n! / (r! × (n - r)!)
Frequently Asked Questions
What is the primary difference between permutations and combinations?
In permutations, the sequence order matters (e.g. a lock code 1-2-3 is different from 3-2-1). In combinations, selection order does not matter (e.g. a hand of playing cards).
What is the formula for permutations (nPr)?
nPr = n! / (n - r)!, where ! denotes factorial (n! = n × (n-1) × ... × 1).
What is the formula for combinations (nCr)?
nCr = n! / (r! × (n - r)!). It divides nPr by r! to eliminate duplicate orderings.
Why this calculator matters
This calculator helps solve mathematical problems faster and with fewer manual arithmetic mistakes. It is useful for studying, research verification, technical engineering checks, and everyday problem-solving.
When to use it
Use it when you need a fast answer, a cross-check for manual calculations, or a clear step-by-step verification of your result.
Quick tips
Double-check your inputs, keep units consistent across all fields, and verify boundary conditions.
Related Math Calculators
Explore more calculators related to this topic to solve other mathematical problems.