A judge chooses a jury of n people out of a pool of N people. The choice is uniform among all subsets of n elements of the pool. Unhappy with an outcome, he dissolves this jury (returning the people into the pool) and chooses another jury of m people, independently of the first jury. What is the probability that the first jury and the second jury have k common people?
(i) Solve the problem in general form.
(ii) Find the decimal value for N = 1000, n = m = 2, k = 1.