Calculadora de Combinações
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
C(n,k) = n! / (k!(n−k)!)
About this calculator
The Combinations Calculator computes the number of ways to choose k items from a set of n items, where order does not matter. The formula used is C(n, k) = n! / (k! (n−k)!), where n! denotes the factorial of n. For example, choosing 3 cards from a 52-card deck yields C(52, 3) possible combinations.
This tool is useful in probability, statistics, and combinatorial mathematics. Common scenarios include calculating lottery odds, forming study groups, selecting teams, or analyzing genetic combinations. Simply enter the values of n (total items) and k (chosen items) to get the result instantly.
Important precautions: n and k must be non-negative integers, with k ≤ n. For large values, the result can be enormous; the calculator handles numbers up to its representation limit. Remember that combinations differ from permutations, where order matters. This calculator considers only combinations.
Frequently asked questions
What is the difference between combination and permutation?
In combinations, order does not matter; in permutations, order matters. For example, choosing 3 numbers from 1 to 10 yields combinations, while arranging them yields permutations.
Can I use decimal values for n or k?
No. n and k must be non-negative integers, with k ≤ n. The factorial formula is defined only for integers.
What if n or k is too large?
The calculator may return a very large number or infinity if it exceeds capacity. For huge values, use approximations or specialized software.
How to calculate combinations with repetition?
This calculator does not support repetition. For combinations with repetition, use the formula C(n+k-1, k).