Question 1152448
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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  {{{C[60]^8}}}.



The favorable set is the combination of all subsets of  5 workers selected from 27 workers of the first shift,  {{{C[27]^5}}}, 

and all subsets of  3  workers selected from 33 workers not belonging to the first shift,  {{{C[33]^3}}}.


Therefore, the probability under the question is


    P = {{{C[27]^5}}}.{{{C[33]^3}}} / {{{C[60]^8}}}.


I leave it to you to make all necessary calculations.
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