 Binomial coefficient

The binomial coefficientcounts the $k$-element subsets of an $n$-element set. Equivalently, it counts strings containing $k$ copies of one symbol and $n-k$ copies of another.

The binomial coefficient, often denoted as \( \binom{n}{k} \) or \( C(n, k) \), is a mathematical expression that represents the number of ways to choose \( k \) elements from a set of \( n \) elements without regard to the order of selection. It is a crucial concept in combinatorics and has applications in probability, statistics, and various fields of mathematics.