PrepZii

table

Permutations, Circular Permutations and Combinations

The source opens with arrangements, circular permutations, and selections.

Counting result	Formula
Permutations of $n$ different things taken $r$ at a time	${}^{n}P_r=n(n-1)(n-2)\cdots(n-r+1)=\frac{n!}{(n-r)!}$
Circular permutations of $n$ different things taken all at a time	$(n-1)!$
Combinations of $n$ different things taken $r$ at a time	${}^{n}C_r=\frac{n!}{r!(n-r)!}=\frac{{}^{n}P_r}{r!}$

$n$

count, index, or number of trials

$r$

selection size, index, or position vector