The subject of this thesis is the Number Problem, a question of distributive justice in which an indivisible benefit or burden must be allocated to one group of individuals at the expense of at least one other group, where the groups contain different people. When these groups differ in size, the Number Problem asks whether the interests of the largest group should always prevail in virtue of the greater number of people that stand to benefit. My answer is that they should not, that we should hold a two-stage weighted lottery to decide what to do. My method begins by assessing the relative loss facing each person in the problem, connecting the strength of a person's claim for aid to the magnitude of the potential loss that they face. Claims are then given a chance of selection in proportion to their relative strengths by way of a lottery in the first stage of my solution. The result of the lottery is then optimized in accordance with the Pareto principle in the second stage, giving the overall result that individuals in larger groups stand a proportionally greater ex ante chance of receiving the good under distribution.The arguments in this thesis divide into two broad thematic sections: arguments in favour of my solution and objections to rival approaches. Included within the former are two arguments that demonstrate how the two-stage weighted lottery result can be derived from the rival positions of equal maximum chances and claim balancing. Similarly, I offer a range of responses to the main objections to the two-stage weighted lottery here. These objections include the 'incredulous stare', the criticism that my solution implausibly gives one person some chance of being saved at the expense of everyone else alive.After considering and rejecting three alternative solutions - equal maximum chances, claim balancing and hybrid - the final part of the thesis addresses the expanded Number Problem where the choice concerns both different sized groups and different potential individual losses. Here I demonstrate that the two-stage weighted lottery approach can solve the most complex expanded Number Problem - even when the choice involves overlapping sets of individuals and different probabilities of successfully aiding each person.