I need an answer for this, show work and notations, therefore statement aswell

4. There are 10 parents, 25 students, and 7 teachers on a school field trip. Eight people are selected at random to win special prizes at the field trip. a) What is the probability that the winners are all students? [2A] b) What is the probability that exactly two are students? [3A] c) What is the probability that exactly three are students and two are teachers? [37] d) What is the probability that at most two teachers are selected? [3T] e) What is the expected number of winners who are: [3A] i) parents? ii) students? iii) teachers