How many terms are in the expansion of $(a + b + c)^4$?

1. The trinomial expansion of $(a + b + c)^n$ uses MULTINOMIAL coefficients: $\binom{n}{i,j,k}\,a^i b^j c^k$ where $i + j + k = n$. 2. Number of terms = number of non-negative integer solutions of $i + j + k = n$. 3. Stars-and-bars formula: $\binom{n + r - 1}{r - 1}$ where $r$ is the number of variables ($r = 3$ here). 4. For $n = 4$, $r = 3$: number of solutions = $\binom{4 + 3 - 1}{3 - 1} = \binom{6}{2} = 15$. 5. So the trinomial $(a+b+c)^4$ has $15$ distinct terms. 6. Option A is the BINOMIAL term count ($n+1$ — wrong for trinomial). Options B and D are wrong stars-and-bars computations. _Source: syllabus Mathematics, Ch 7, §7.2 + Exercise (extension to trinomials), p. 8._