User:IssaRice/Summary of counting techniques: Difference between revisions

Revision as of 02:12, 14 August 2019

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

@@ Line 6: / Line 6: @@
 | || <math>\{(a_1, \ldots, a_k) : a_1,\ldots, a_k \in A\}</math> ||
 |-
-| || <math>\{{a_1, \ldots, a_k} : a_1,\ldots, a_k \in A\}</math> ||
+| || <math>\{\{a_1, \ldots, a_k\} : a_1,\ldots, a_k \in A\}</math> ||
 |-
 | || <math>\{(a_1, \ldots, a_k) : a_1,\ldots, a_k \in A \text{ and all }a_i\text{ distinct}\}</math> ||