Combinatorics Calculator
Calculate permutations, combinations, repeated permutations, and multiset combinations from n and r.
Category: Calculators
When to use?
Use it to count ways to pick 3 people from 5, estimate password combinations, or calculate sample-space sizes for probability problems.
How to use
- Enter n, the total number of items.
- Enter r, the number of selected items.
- Compare permutation, combination, and repeated-selection results.
Input Explanation
n and r must be non-negative integers. For ordinary permutations and combinations, r cannot exceed n.
Calculation Basis
P(n,r) = n!/(n-r)!, C(n,r) = n!/(r!(n-r)!), repeated permutation = n^r, and multiset combination = C(n+r-1, r).
Usage Examples
- Probability calculations - Count the size of a sample space before calculating probability.
- Password estimates - Estimate how many possible codes a rule can generate.
Examples
- P(5,3) = 60
- C(5,3) = 10
- A 4-digit password using 10 digits with repeats allowed has 10^4 = 10,000 possibilities
FAQ
What is the difference between permutation and combination?
Permutations care about order, so ABC and BAC are different. Combinations ignore order, so they are the same selection.
What does repeated combination mean?
It counts selecting r items from n types when repeats are allowed and order does not matter.
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