Number of Distinct Terms in Expansion

The number of distinct terms in the expansion of $(x_1 + x_2 + \dots + x_r)^n$ is given by: $\binom{n + r - 1}{r - 1}$

For $(a + b + c)^{20}$, $n = 20$ and $r = 3$: $\text{Number of terms} = \binom{20 + 3 - 1}{3 - 1} = \binom{22}{2} = \frac{22 \times 21}{2} = 231$.