Question: Five of the 15 school buses of a particular school district will be selected for thorough inspection. Suppose four of the buses have developed a slight defect since their last inspection (the steering wheel shakes when braking).
(a) How many possible selections are there?
(b) How many selections contain exactly three buses with the defect?
(c) If the five buses are selected by simple random sampling, what is the probability the sample includes exactly three of the buses with the defect?
(d) If the buses are selected by simple random sampling, what is the probability all five buses are free of the defect?