Calculadora de Coeficiente Binomial
- 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 Binomial Coefficient Calculator computes the number of combinations of n items taken k at a time, denoted as C(n,k) or n choose k. It tells how many subsets of size k can be formed from a set of n distinct elements, disregarding order. The formula uses factorials: C(n,k) = n! / (k! (n−k)!).
To use the calculator, enter non-negative integers n and k, with k ≤ n. It is useful in probability, statistics, and combinatorics, for example, to determine lottery odds, poker hand counts, or team combinations. The tool handles large numbers through factorial optimizations.
Note: k must not exceed n; otherwise, the result is zero. For very large values (above 1000), calculation may be slow or cause overflow. The calculator assumes n and k are non-negative integers. Remember that C(n,k) = C(n, n−k), which can simplify computations.
Frequently asked questions
What does C(n,k) mean?
C(n,k) is the number of combinations of n items taken k at a time, i.e., how many distinct groups of k elements can be formed from n total elements, disregarding order.
Can I use k greater than n?
No. If k > n, the binomial coefficient is zero because you cannot choose more elements than available.
How to calculate C(5,2) manually?
Use the formula: 5! / (2! (5−2)!) = 120 / (2 * 6) = 120 / 12 = 10. That means there are 10 ways to choose 2 items from a set of 5.
What is the relation to Pascal's triangle?
Binomial coefficients form Pascal's triangle, where each number is the sum of the two above. C(n,k) corresponds to the entry in row n and column k.
What if the result is too large?
For large values, the number may have many digits. The calculator displays the exact result, but some browsers may truncate it. Use scientific notation if needed.