A management facility divides workdays into 3 shifts â EarlyBird, Cricket and NightOwl. The facility recently hired 20 workers on the EarlyBird shift, 15 workers on the Cricket shift, and 10 workers on the NightOwl shift. Six of these workers are to be chosen for rigorous interviews. Suppose the selection is made in such a way that any particular group of six workers has the same chance of being selected as does any other group (that is, drawing choices without replacement) Required:
a. In how many ways can all six interviewees come from the EarlyBird shift? What is the probability of that happening?
b. The facility manager is concerned that choosing 6 workers randomly might result in all interviewees coming from the same shift. Is this a valid concern? Explain.
c. How likely is it that interviewees come from at least 2 of the shifts?
d. The manager is concerned that at least one shift might not be represented. What is the probability of that happening?