Probablility question: I have no idea where to even start?

A production facility employs 20 workers on the day shift, 15 workers on the swing shift, and 10 workers on


the graveyard shift. A quality control consultant is to select 6 of these workers for in-depth interviews. Suppose


the selection is made in such a way that any particular group of 6 workers has the same chance of being selected


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?


b. What is the probability that all 6 selected workers will be from the same shift?


c. What is the probability that at least two different shifts will be represented among the selected workers?


d. What is the probability that at least one of the shifts will be unrepresented in the sample of workers?

Probablility question: I have no idea where to even start?
nCr is the number of ways of taking r objects from a set of n.





a. the probability you need is 20C6 / 45C6. the numerator is the answer for the number of selections.





b. answer: [20C6 + 15C6 + 10C6] / 45C6





c. the answer is the complement of b.


1 - "answer of b". ... it can also be written as [45C6 - 20C6 - 15C6 - 10C6] / 45C6





d. its complement is the event where all shifts are represented. to get that choose one worker from each shift.


then randomly choose the others from the whole group.


20*15*10*42C3 / 45C6 ... this is the representation of the complement.


so the answer is


[45C6 - 20*15*10*42C3] / 45C6








§
Reply:a. 20-choose-6 = 38760 and


20-choose-6 / 45-choose-6 = 38760 / 8145060 = 0.476%





b. 20-choose-6 + 15-choose-6 + 10-choose-6 over 45-choose-6 = (38760 + 5005 + 210) / 8145060 = 0.540%





c. This one is so complex I'd need a program to solve it. "At least" means you need to sum a series of combinatorial values.





d. Again, this one requires a computer program. Again, the "at least" condition makes the question very hard.





[Gees, what kind of class are you in?]