How to check if $n!$ is $ O(2^n)$ How can I check if $n! \in O(2^n)$?
The definition of $f$ being $O(g)$ is  $f(n) \le c g (n)$, where $c>0$.
So it would mean $n!  \le  c  2^n$.
What is the clearest way to solve this? (As I am solving the past papers for my next examen.)
Thank you!

It is not.  Intuitively, $n!$ has $n$ factors and most of them are larger than $2$.  The ratio gets larger and larger, so you should expect $\frac {n!}{2^n}$ to grow without bound.  
A very simple proof by induction is that $\frac {4!}{2^4} \gt 1$.  Assume $\frac {k!}{2^k} \gt 1,$ then $\frac {(k+1)!}{2^{k+1}} \gt \frac {k+1}2$ which grows without bound.
