<s>[INST] Find the coefficient of $x^3y^2z^3w$ in the expansion of $(2x+3y-4z+w)^9$ 
Find the coefficient of $x^3y^2z^3w$ in the expansion of $(2x+3y-4z+w)^9$

Using the formula of multinational coefficients
$$
        \begin{pmatrix}
        n \\
        r_1,r_2,...,r_k  \\ 
        \end{pmatrix}= \ \frac{n!}{r_1! \cdot r_2! \cdot  \ldots \cdot r_k!}  \
$$
$$\Rightarrow  \begin{pmatrix}
        9 \\
         3, 2, 3, 1  \\ 
        \end{pmatrix}= \frac {9!}{3!2!3!1! } =  \bbox[yellow]{5040} $$
Would the above be the answer or does one have to take this one step further by further expanding?
$$ 5040 *(2)(3)(-4)(1) = -120960$$ 
 [/INST] $5040 \times 2^3 \times 3^2 \times (-4)^3 \times 1 =-23224320$
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