Whether family members of the organizer were excluded has no bearing on whether the remaining entrants all had an equal chance of winning. The fairness requirement concerns each entrant's chance of winning, not the eligibility rules governing who may enter.

Knowing how the winner would be selected might sound connected to fairness, but transparency is a separate issue from whether the lottery actually gave everyone an equal chance. Even if every entrant could know exactly how the selection would work, we still have no idea whether the selection process gave some entrants a higher chance of winning than others.

Remember, one alternate explanation for the fact that 90% of winners were entrants from the first 2 days is the possibility that the vast majority of entrants just happened to submit their entry forms in the first 2 days. (C) eliminates that explanation and therefore strengthens the author's argument. If entries came in at a consistent rate across all 30 days, then early entrants made up only a small fraction of all entrants. Yet 90% of winners came from that small group. This strongly suggests that they really did have a higher chance of winning than other entrants.

Like (B), this concerns transparency rather than the entrants' chances of winning. Posting the rules conspicuously tells us that entrants could learn what the rules were. But we still have no idea whether the way winners were selected gave some entrants a higher chance of winning than others.

How the actual turnout compared to the organizers' expectations has no bearing on whether those entrants all had an equal chance of winning. Whether 100 people or 100,000 people entered, the relevant question is whether each person, however many there were, had the same chance of winning.