## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$18278$
$n$ objects in $r$ spots where each spot can contain any of the objects is $n^r$. Thus the number of $1$ letter long company names: $26^1=26$ Thus the number of $2$ letter long company names: $26^2=676$ Thus the number of $3$ letter long company names: $26^3=17576$ Thus in total: $26+676+17576=18278$