Question: 2015 Fall Final - 6
Consider strings of characters, each character being $a$, $b$, or $c$, that contain at least one $a$.
Let $S_n$ be the number of such strings having length $n$. Which of the following is true?
(a)
$S_n = n \cdot 3^{n-1}$
(b)
$S_n = 3^{n} - 2^{n}$
(c)
$S_n = 3^{n} - n$
(d)
$S_n = n \cdot 2^{n-1}$