Suppose that 8 applicants from the Austin location and 7 applicants from the Boston location have applied for positions at the Charlotte headquarters, where a total of 7 applicants will be selected for new positions.

(a) If 7 positions are filled at random, what is the probability of selecting 3 people from Boston and 4 people from Austin?

(b) If 7 positions are filled at random, what is the probability of selecting 2 people from Boston and 5 people from Austin?

(c) If 7 positions are filled at random, what is the probability of selecting 7 people from Boston?