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?

b) What is the probability that exactly two are students?

c) What is the probability that exactly three are students and two are teachers?

d) What is the probability that at most two teachers are selected?

e) What is the expected number of winners who are:

i) parents? ii) students? iii) teachers?