If Pascal's Triangle begins with row zero, then row $ n $ has $ n+1 $ elements and the sum of the elements in row $ n $ is $ 2^n $. So when $ n=3 $, the row has four elements and the sum of the elements is $ 2^3=8 $. For $ n=10 $, the sum of the elements is $ 2^{10}=\boxed{1024} $.