Question

[Statistics] A production facility employs 10 workers on the day shift, 8 workers on the swing shift, and 6 workers on the graveyard shift. A quality control consultant is to select 4 of these workers for in-depth interviews. Suppose the selection is made in such a way that any particular group of 4 workers has the same chance of being selected as does any other group

Answer 1

What is the probability that one of the shifts will be unrepresented in the sample of workers?

Answer 2

I got that there are (24)(23)(22)(21)/(4)(3)(2) = 10626 possibilities

(18)(17)(16)(15)/(4)(3)(2) = 3060 possibilities where graveyard is unrepresented
(16)(15)(14)(13)/(4)(3)(2) = 1820 possibilities where swing is unrepresented
(14)(13)(12)(11)/(4)(3)(2) = 1001 possibilities where day is unrepresented

So the total probability is (3060+1820+1001)/10626 = .5535, which is incorrect.