Combination

A selection of elements from a Set where order doesn’t matter. “n choose k”.

$$C(n,k)=C_{n,k}=\left(\begin{array}{c}n\\ k\end{array}\right)=\frac{n!}{k!(n-k)!}=\frac{P(n,k)}{P(k,k)}$$

It is also called “Binomial Coefficient”, as it forms the terms in Pascal’s Triangle, which are coefficients of $n^{\text{th}}$ degree binomial when expanded into a Polynomial.

Stars and Bars

How many ways are there to seperate some amount of stars with some amount of bars?

$$C(\star +┃,┃)$$