l) (28 points - 21 minutes) Because of their deep concern about grade ination, the faculty members at Bill's College have decided course grades should be assigned at random. There are 12 students taking the course "Economics of Antarctica," 4 of whom are Caucasian, 5 of whom are Asian or Asian-American, and 3 of whom are African-American. According to the rules of the college, 4 students in this class will be chosen to receive an A, 6 will receive a B, and 2 will receive a C (Bill's College has no pluses and minuses). a) How many different grade assignments are possible? b) Let A be the event that both students chosen to receive C grades are Caucasian and let B be the event that none of the students chosen to receive C grades are African-American Determine P(A). c) Are A and B mutually exclusive? (Justify your answer.) d) Are A and B independent? (Justify your answer.)