In the expansion of $(a + b)^n$ there are $n + 1$ dissimilar terms. The number of dissimilar terms in the expansion of $(a + b + c)^{10}$ is:
$\textbf{(A)}\ 11\qquad  \textbf{(B)}\ 33\qquad  \textbf{(C)}\ 55\qquad  \textbf{(D)}\ 66\qquad  \textbf{(E)}\ 132$
Expand the binomial $((a+b)+c)^n$ with the binomial theorem. We have:
\[\sum\limits_{k=0}^{10} \binom{10}{k} (a+b)^k c^{10-k}\]
So for each iteration of the summation operator, we add k+1 dissimilar terms. Therefore our answer is:
\[\sum\limits_{k=0}^{10} k+1 = \frac{11(1+11)}{2} = 66 \to \boxed{\textbf{D}}\]