7.6 Advanced Extension: Multinomial Theorem

We check if powers sum to $n$: $3+4+2 = 9$. Yes. Using Multinomial Coefficient formula: $\text{Coeff} = \frac{n!}{p_a! p_b! p_c!} = \frac{9!}{3! 4! 2!}$ $= \frac{362880}{6 \cdot 24 \cdot 2} = \frac{362880}{288} = 1260$.