Notice that there are 27+19+14 = 60 workers, in all.

Of them, 19+14 = 33 are from the second and the third shift, together.


The full sample space in this case is the set of all subsets of 8 workers selected from 60 workers.

The number of such subsets is  .



The favorable set is the combination of all subsets of  5 workers selected from 27 workers of the first shift,  , 

and all subsets of  3  workers selected from 33 workers not belonging to the first shift,  .


Therefore, the probability under the question is


    P = . / .


I leave it to you to make all necessary calculations.