An $r$-combination of elements of a [[Set]] is an unordered selection of $r$ elements from the set. An $r$-combination is just a $r$-element [[Subset]] of a given [[Set]] The number of $r$-combinations of a [[Set]] with $n$ elements, where $n$ is an [[Integer]] with $n\ge 0$, and $r$ is an integer with $0\le r\le n$ is: $\huge C(n,r) = \frac{n!}{r!(n-r)!} $ $ P(n,r)= \underbrace{C(n,r)}_\text{\# of r-element subsets} \cdot \underbrace{P(r,r)}_\text{\# of ways of ordering } $