Mary, who wrote an online computer game, plans to assign every user a unique password.
a) Currently, she wants to have passwords that are \(8\) symbols long and are all made from lowercase letters \(a,b,c\). How many different passwords can she generate?
b) Her friend suggested a modification: use 8-symbol words made from letters \(a,b,c\), with exactly one capital letter, and also include one digit (\(0-9\)). How many times more passwords can she generate now?