Question

A warehouse employs 27 workers on first shift and 18 workers on second shift. Eight workers are chosen at random to be interviewed about the work environment. Complete parts​ (a) through​ (d). ​(a) Find the probability of choosing all​ first-shift workers.

Answer 1

Solution:
Since we are interested in the order of the people chosen, order is not important and thus we need to use a combination.

we will be selecting 8 out of 27 + 18 = 45

45C8 = 45!/(8!*(45-8)!) = 45!/(8!*37!) = 215553195

we are interested in how many ways result in 8 people being selected from the 27 workers on the first shift.

27C8 = 27!/(8!*(27-8)!) = 27!/(8!*19!) = 2220075

The probability is the number of favorable outcomes divided by the number of possible outcomes.

P(all first-shift workers) = number of favorable outcomes/number of possible outcomes
= 2220075/215553195
= 0.0102