Counting Methods

Permutations

“The number of size k ordered tuples from N options” (sampling without replacement)

$$P_{n,k}=\frac{n!}{(n-k)!}$$

Combinations

“The number of size k subsets from N options” (sampling without replacement)

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

Possible order of n items

$$n!$$