The four basic combinatoric formulas? There are 4 basic combinatoric formulas when picking $k$ elements among $n$
We have repetition is allowed or not allowed, and order matters or does not matter.
When order matters and repetition is not allowed we call it a permutation.
When order does not matter and repetition is not allowed we call it a combination.
What are the names of the missing two and what are the formulas for each?
 A: We have the following cases for the number  of subsets of size $k$ chosen from a set of $n$ distinct elements:


*

*replacement and ordered, "permutation with repetition" $$n^k$$

*no replacement and ordered, "k-permutations of n" $$\frac{n!}{(n-k)!}$$

*no replacement and unordered, "combinations" $$\binom{n}k$$

*replacement and unordered, "combination with repetitions" $$\binom{n+k-1}k$$
A: When order matters and repetition is allowed, you get all the functions from $\{1,2, \cdots, k\}$ to your set $S$ of $n$ elements.   Every function corresponds to a unique choice, and every choice allows you to construct a function by setting $f(r)$ to be the $r^{th}$ element chosen.  The formula for these is simpler, just being $n^k,$ because we have a full $n$ independent choices to make, $k$ times in a row. 
Perhaps the most complicated of the four is when repetition is allowed but order does not matter.  Those are called multisets.  There is an explicit formula for $n$ multichoose $k$ given by $\left( {n \choose k}\right) = {n+k-1 \choose k}.$ 
