How many 5 letter different words can be formed using the letters AAASSSBB I saw that these sort of questions have been asked before, but not exactly this kind of problem: creating 5 DIFFERENT words, not just all possible combinations.
The words don't need to have any meanings.
I'd appreciate an explanation in addition to the solution.

$$
\begin{array}{c|c|c}
\text{Letters}  & \text{Calculation} & \text{# Possibilities}\\
\hline\\
AAASS &  \displaystyle\binom{5}{3} & 10 \\\\
AAASB &  \displaystyle\binom{5}{3} \cdot 2 & 20\\\\
AAABB &  \displaystyle\binom{5}{3} & 10\\\\
AASSS &  \displaystyle\binom{5}{2} & 10\\\\
AASSB &  \displaystyle\binom{5}{2} \cdot \binom{3}{2} & 30\\\\
AASBB &  \displaystyle\binom{5}{2} \cdot 3 & 30\\\\
ASSSB &  5\cdot \displaystyle\binom{4}{3} & 20\\\\
ASSBB &  5\cdot \displaystyle\binom{4}{2} & 30\\\\
SSSBB &  \displaystyle\binom{5}{3} & 10\\\\
\end{array}
$$

This gives a total of $$\boxed{170}$$
