Can someone please explain why the ansewr is 12? My current working: Using the multinomial theorem, each term in the expanded (unsimplified) form would be uniquely determined by its distinct ordered partition of n, $x_1+x_2+...+x_m$.
And so the and so given n=8, the number of partitions and hence terms in the expanded multinomial is $\begin{pmatrix} 9 \\ 4\end{pmatrix}$.
Is this reasoning correct? Because 126 total terms seems like a lot. And, if according to my previous reasoning, were each unique partition of $n$ determines a separate multinomial coefficient (and hence term), wouldn't that mean that the term with $\begin{pmatrix} 8 \\ 2,4,0,2\end{pmatrix}$ should be unique?