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In the expansion of $(x-2 y+3 z)^5$, if the total number of terms is $p$ and the coefficient of $x^2 y z^2$ is $q$, then $\frac{q}{p}=$
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The correct answer is:
$60$
$(x-2 y+3 z)^5$
Total number of terms $={ }^{5+3-1} C_{3-1}={ }^7 C_2$
$$
\therefore \quad p=21
$$
Coefficient of $x^2 y z^2=\frac{5 !}{2 ! \cdot 1 ! \cdot 2 !}(1)^2(-2)^1(3)^2$
$$
\begin{aligned}
& \therefore \quad q=-540 \\
& \therefore \quad \frac{q}{p}=\frac{-540}{21}=\frac{-180}{7} .
\end{aligned}
$$
Total number of terms $={ }^{5+3-1} C_{3-1}={ }^7 C_2$
$$
\therefore \quad p=21
$$
Coefficient of $x^2 y z^2=\frac{5 !}{2 ! \cdot 1 ! \cdot 2 !}(1)^2(-2)^1(3)^2$
$$
\begin{aligned}
& \therefore \quad q=-540 \\
& \therefore \quad \frac{q}{p}=\frac{-540}{21}=\frac{-180}{7} .
\end{aligned}
$$
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