A student-faculty government committee of 4 people is to be formed from 20 student volunteers and 5 faculty volunteers.

a. If one person from the group of volunteers is chosen at random to draw the names out of a hat, what is the probability that the person drawing the names is a student?

b. How many ways can the committee of four be formed if there are no restrictions on composition.

c. How many ways can two of the students be chosen?

d. How many ways can 2 faculty be chosen?

e. What is the probability that the random selection of the four-person committee will result in two students and two faculty?

(please show work)