3. A wine collector has r distinguishable bottles of red wine and w distinguishable bottles of white wine; after putting on a blindfold the collector lines up the bottles in her collection at random, so that each ordering of the bottles is assumed equally likely. (a) Describe the sample space and compute its cardinality in terms of r and w. (b) Compute the probability that the bottle in the ith position, 1 g 1' g r + w, is a bottle of red wine. 4. Consider a 6 X 6 matrix, in which we randomly choose 6 among its 36 entries to be \"1", while the remaining entries are \"0\". Compute the probability that each row and each column of the matrix contains exactly one 1