\dbinom{n}{k}

The binomial coefficient, denoted as \( \dbinom{n}{k} \), 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 fundamental concept in combinatorics and is used in various mathematical calculations, including probability and algebra.

Examples

Choosing 2 elements from a set of 5 elements.

\dbinom{5}{2} = 10

There is exactly one way to choose 0 elements from a set of n elements.

\dbinom{n}{0} = 1

There are n ways to choose 1 element from a set of n elements.

\dbinom{n}{1} = n