Originally Posted by

**Chris11** Hey guys, I just learned about combinatorical style proofs. Anyways, I was wondering if you could just tell me if the following proof of mine is acceptable.

Claim: $\displaystyle n\choose 0 $ + $\displaystyle n\choose 1 $+...+$\displaystyle n\choose n$=$\displaystyle 2^n$

Proof. The left hand side and the right hand side count the number of subsets of an n element set. We need to show that the RHS is equilivent to the LHS. We do this as follows. Take an arbitrary subset of the n element set. We need to determine whether or not each element of the n set is in this subset. This gives us

2x2x2x...x2=$\displaystyle 2^n$ possibilities. Hence, RHS=LHS.