$14\mathrm{.}1$: Counting accepted strings

Let M be a DFA with alphabet $\{$a$,$ b$\},$ state set $\{$p$,$ q$\},$ start state p$,$ final state set $\{$q$\},$ and transition function given by $($p$,$ a$)=$ $($q$,$ a$)=$ q and $($p$,$ b$)=$ $($q$,$ b$)=$ p$.$ Then L$($M$)$ has exactly eight strings with three or fewer letters.