A warehouse employs 24 workers on first shift, 18 workers on second shift, and 14 workers on third shift. Eight workers are chosen at random to be interviewed about the work environment. Find the probability of choosing exactly five first-shift workers.
The probability of choosing exactly five first-shift workers is (Round to three decimal places as needed.)

Step 1 ：The total number of workers is 24 (first shift) + 18 (second shift) + 14 (third shift) = 56 workers.

Step 2 ：The number of ways to choose 8 workers out of 56 is given by the combination formula \(C(n, k) = \frac{n!}{k!(n-k)!}\), where n is the total number of items, k is the number of items to choose, and '!' denotes factorial.

Step 3 ：The number of ways to choose exactly 5 first-shift workers out of 24 is also given by the combination formula.

Step 4 ：The number of ways to choose the remaining 3 workers out of the remaining 32 workers (56 total - 24 first shift) is also given by the combination formula.

Step 5 ：The probability of choosing exactly five first-shift workers is then the number of ways to choose 5 first-shift workers and 3 non-first-shift workers divided by the total number of ways to choose 8 workers.

Step 6 ：Calculating these values, we find that the total number of ways to choose 8 workers is 1420494075, the number of ways to choose 5 first-shift workers is 42504, and the number of ways to choose the remaining 3 workers is 4960.

Step 7 ：Thus, the probability is \(\frac{42504 \times 4960}{1420494075} = 0.1484130372032703\).

Step 8 ：Final Answer: The probability of choosing exactly five first-shift workers is approximately \(\boxed{0.148}\).