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If $10{ }^n C_2=3^{n+1} C_3$, then the value of $n$ is
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The correct answer is:
$9$
$10^n C_2=3^{n+1} C_3$
$\frac{10 n !}{(n-2) ! 2 !}=\frac{3(n+1) !}{(n+1-3) ! \times 3 !}$
$\begin{aligned} \Rightarrow & & \frac{10 n !}{2} & =\frac{3(n+1) n !}{3 \times 2} \\ \Rightarrow & & 10 & =n+1 \\ \Rightarrow & & n & =9\end{aligned}$
$\frac{10 n !}{(n-2) ! 2 !}=\frac{3(n+1) !}{(n+1-3) ! \times 3 !}$
$\begin{aligned} \Rightarrow & & \frac{10 n !}{2} & =\frac{3(n+1) n !}{3 \times 2} \\ \Rightarrow & & 10 & =n+1 \\ \Rightarrow & & n & =9\end{aligned}$
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