I need some help starting this problem. Is this a Weak Law of Large Numbers problem, where you add 500 iid random variables to form an approximate normal distribution? Or something different?

(a) Suppose that in an interval [0,1000], 500 points are independently placed, each uniformly at random. Let N denote the number of points that fall into the interval [0,10]. (i) Provide the exact distribution of P(N = n) for n = 0,1,2.... Explain your reasoning.