Compute $\lim_{n \rightarrow \infty} \ln \frac{n!}{n^n}$

Note that 
\[\lim_{n \rightarrow \infty}\frac{n!}{n^n}=\lim_{n \rightarrow \infty}\frac{1}{n}\times \frac{2 \times 3 \times 4\times \dots \times n}{n \times n \times \dots \times n}\leq \lim_{n \rightarrow \infty}\frac{1}{n} =0.\]
So 
\[\lim_{n \rightarrow \infty}\frac{n!}{n^n}=0,\]
and 
\[\lim_{n \rightarrow \infty}\ln \frac{n!}{n^n}=- \infty.\]