Combination Problem

Homework Statement

Solve for n.
$$11_{C}_n=330$$

Homework Equations

$$n_{C}_r=\frac{n!}{(n-r)!r!}$$
Sorry if the combination formula looks bad. I don't know how to write the comb. formula with Latex.

The Attempt at a Solution

I solved for n as far as $$n!(11-n)!=133056$$ How do I go further with this? The answers are 4 or 7.

$$_{11}C_n = \frac{11!}{n!(11-n)!} = 330 \implies n!(11-n)! = \frac{11!}{2 \cdot 3 \cdot 5 \cdot 11}$$
$$n!(11-n)! = 3 \cdot 8!$$