Matching problem (case of sampling without replacement). Show that for j = 1, ...,M the conditional probability of a match in the jth urn, given that there are m matches, is m/M. Show, for any 2 unequal integers j and k, 1 to M, that the conditional probability that the ball number j was placed in urn number k, given that there are m matches, is equal to (M - m)(M - m - l)/M(M - 1).