Hi .

Can Anyone help to proof $\displaystyle \sum C(n,r)=2^n$ without using

sets .

I am Wondering how to Solve this Series?

$\displaystyle \sum_{r=0}^{n} \frac{n!}{r!(n-r)!}$

............

I Know :

$\displaystyle \sum_{r=0}^{n} \frac{n!}{r!(n-r)!} = n!\sum_{r=0}^{n} \frac{1}{r!(n-r)!}$