Binomial coefficient

The binomial coefficient is a function of two integers ${\displaystyle n}$ and ${\displaystyle k}$. It represents the number of possible ways to choose ${\displaystyle k}$ things from ${\displaystyle n}$ possible options, without repeating any options or caring about the order in which they are chosen. The binomial coefficient counts the number of combinations of size ${\displaystyle k}$ exist on ${\displaystyle n}$ objects. It is called the binomial coefficient because it occurs in binomial expansion.