Dr. Agarwal buys a box of 12 ice cream sandwiches in assorted flavors, with 5 vanilla, 4 mint chip, and 3 neopolitan. Suppose that she eats an ice cream sandwich after dinner each night for 3 nights in a row, selecting uniformly at random from the box each time. (a) (3 points) What is the probability that she eats the same flavor all three nights? (b) (4 points) Let M be the number of mint chip ice cream sandwiches she eats, and let N be the number of neopolitan ice cream sandwiches she eats. Find thejoint PMFpMW (j, k) for j and k in {0, 1, 2, 3}. Hint: it is probably easier to write out an explicit formula in j and is: rather than writing a 4 X 4 table