Binomial Coefficient Calculator
Understanding Binomial Coefficients
The binomial coefficient, written as \(C(n, k)\), \(_nC_k\), or \(\binom{n}{k}\), represents the number of ways to choose \(k\) elements from a set of \(n\) elements, where the order of selection does not matter. This is also known as a combination.
- \(n\) (Total Items): The total number of items in the set. Must be a non-negative integer.
- \(k\) (Items to Choose): The number of items to choose from the set. Must be a non-negative integer, and \(k \le n\).
Formula
The binomial coefficient is calculated using the formula:
\[ \binom{n}{k} = \frac{n!}{k!(n-k)!} \]
where \(n!\) denotes the factorial of \(n\).
Calculates "n choose k" combinations.
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