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 \(\boxed{0.148}\).