How do you describe the sample space of a lottery (49 balls, 6 draws without replacement)? Sample space = {1,2,3...49}^6 where sample point w_i is removed after each draw doesn't sound that mathematical. Is there a correct way to write it?

Final outcome is we have six balls, those can be any but each is unique and ditinct and remaining 49-6=43 balls remian in box. So sample space contains:
$$\zeta=\{(1,2,3,4,5,6),(1,2,3,4,5,7),(1,2,3,4,5,8),...\}$$
and these would be 6-tuples of all possible combinations of 49 balls i.e. ${{}^{49}{\mathbb C}_{6}}$
