Students offered five $(5)$ cooperative training programs at local companies and twelve $(12)$

training programs outside the state. Count the number of possible training opportunities if an

opportunity consists of training at

$($a$)$ One local company or one company outside of the state.

$($b$)$ One local company and one company outside of the state.

$($a$)$ One local company or one company outside of the state. $=5+12=$

$($b$)$ One local company and one company outside of the state. $=5*12=$