why does the number three repeats in many places in the story?

Yes, there is a lot of the number three in the story. Three is a very auspicious number in myth-based stories. There are three members of the White family, there are three wishes...I think that the number three illustrates the danger of messing around with fate. Consider that the first wish is for greed (money), the second wish is for something more substantial and the final wish is to sort out the mistakes from the first two wishes.