Can someone help me do this limit? $ \lim_{n\to\infty} \frac{n!\times(2n)!}{(3n)!}$ can someone help me with this limit?
I don't know how to expand that factorial multiplication, so what I've done so far is substitute what given:

$$ \lim_{n\to\infty} \frac{n!\times(2n)!}{(3n)!}$$
  $$ \lim_{n\to\infty} \frac{\infty\times\infty}{\infty}$$

And with this I can apply the Cauchy or L'Hôpital's theorem by deriving both sides of the fraction independently, but my problem also stars here because, I don't how to derive a factorial term.
Can someone help me please?
Thanks

Hint:
$$\frac{n! (2n)!}{(3n)!} = \prod_{i=1}^{n}\frac{i}{2n+i},$$ and
$$\frac{i}{2n+i} \le \frac{1}{3}.$$
