A production facility employs 20 workers on day shift, 15 workers upon the swing shift, and 10 workers on graveyard shift. A quality control consultant is to choose 6 of these workers for in-depth interviews. Assume the selection is made in such a manner that any particular group of 6 workers has the same chance of being chosen as does any other group (drawing 6 slips without replacement from among 45).
(a) How many selections result in all 6 workers coming from the day shift?
What is the probability that all 6 selected workers will be from the day shift? (Round your answer to four decimal places.)
(b) What is the probability that all 6 selected workers will be from the same shift? (Round your answer to four decimal places.)
(c) What is the probability that at least two different shifts will be represented among the selected workers? (Round your answer to four decimal places.)
(d) What is the probability that at least one of the shifts will be unrepresented in the sample of workers? (Round your answer to four decimal places.)