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
	${(a_{1}, \dots, a_{k}) : a_{1}, \dots, a_{k} \in A}$
	${a_{1}, \dots, a_{k} : a_{1}, \dots, a_{k} \in A}$
	${(a_{1}, \dots, a_{k}) : a_{1}, \dots, a_{k} \in A and all a_{i} distinct}$
	${{a_{1}, \dots, a_{k}} : a_{1}, \dots, a_{k} \in A and all a_{i} distinct}$
	${(a, b) : a \in A and b \in B}$