Question

35. 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

Answer 1

38760 selections result in all 6 workers coming from the day shift.

Explanation:

The order in which the workers are chosen is not important, which means that we use the combinations formula to solve this question.

Combinations formula:

`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

a. How many selections result in all 6 workers coming from the day shift:

20 workers are employed on the day shift, so this is a combination of 6 from a set of 20.

`C_(20,6) = (20!)/(6!(20-6)!) = 38760`

38760 selections result in all 6 workers coming from the day shift.