Words avoiding letters

Direct. Words over $\{b,c\}$: $2^4=16$.

IE check. $|A_1|$ (a in position 1): $3^3=27$; $|A_1\cap A_2|$: $3^2=9$; etc. $|A_i|=27$, $|A_i\cap A_j|=9$, $|A_i\cap A_j\cap A_k|=3$, $|A_1\cap\cdots\cap A_4|=1$.

IE: $81-4\cdot27+6\cdot9-4\cdot3+1=81-108+54-12+1=16$. ✓

Conclusion. $16$ words.