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!

You're close:
$$(1+x)^n = \sum_{k=0}^n\binom{n}{k}x^k$$
If you put $x=1$ in this you get $$(1+1)^n = \sum_{k=0}^n\binom{n}{k}1^k$$
i.e.
$$2^n = \sum_{k=0}^n\binom{n}{k}$$
