User:IssaRice/Summary of counting techniques

Let $A$ be a set with $n$ elements, and let $B$ be a set with $m$ elements.

Description	Set representing counting problem	number of ways to count
	$\{(a_{1},\ldots ,a_{k}):a_{1},\ldots ,a_{k}\in A\}$
	$\{{a_{1},\ldots ,a_{k}}:a_{1},\ldots ,a_{k}\in A\}$
	$\{(a_{1},\ldots ,a_{k}):a_{1},\ldots ,a_{k}\in A{\text{ and all }}a_{i}{\text{ distinct}}\}$
	$\{\{a_{1},\ldots ,a_{k}\}:a_{1},\ldots ,a_{k}\in A{\text{ and all }}a_{i}{\text{ distinct}}\}$
	$\{(a,b):a\in A{\text{ and }}b\in B\}$