The binomial coefficient, also known as the "\(\binom{n}{k}\)" or "nCr" formula, is used to determine the number of ways to choose k items from a set of n items without regard to the order of selection. It is a fundamental concept in combinatorics and probability theory.
The formula for the binomial coefficient is given by:
\[ \binom{n}{k} = \frac{n!}{k!(n-k)!} \]
Where:
\(n\) is the total number of items
\(k\) is the number of items to choose
\(n!\) (n factorial) is the product of all positive integers up to n
\(k!\) (k factorial) is the product of all positive integers up to k
\((n-k)!\) (\((n-k)\) factorial) is the product of all positive integers up to \((n-k)\)