$\begin{align*} \displaystyle{\lim_{n \to \infty} \begin{pmatrix} \frac{(n+1) (n+2) ...3n}{n^{2n}} \end{pmatrix} }^{1/n} \end{align*}$ is equal to :

Question

( A ) $\frac{9}{e^2}$
( B ) $3 \log 3 - 2$
( C ) $\frac{18}{e^4}$
( D ) $\frac{27}{e^2}$