Prove $ \sum_{x=0}^n \binom{n}{x} = 2^n$ using binomial expansion? Right or wrong? I am in a probability and statistics class.  This is one of the first proofs we are supposed to do I am not sure where to start.  I have done some research and I have seen proof by induction for problems like this and also Pascal's Triangle.  I am just not sure if there is a specific way I should be proving this is my specific course.  We have covered basic probability and this problem comes from a section on an introduction to discrete random variables.    
Prove $$ \sum_{x=0}^n \binom{n}{x} = 2^n$$
Here is how I would start:
$2^n = (1 +1)^n = \sum_{x=0}^n \binom{n}{x}1^01^{n-0}$ 
using the binomial expansion... is this the right way to start? or am I totally off? I would appreciate a very basic explanation of this!

One way is
$$
(1+t)^n = \sum_{x=0}^n {n \choose x} t^n
$$
and let $t = 1$.
Another way is to simply note that you are counting all subsets of a set of size n, and there are clearly 2^n of those since each subset is uniquely formed by making one of 2 choices for each element (inclusion or exclusion in the set).
