An engineering company has four openings and the applicant pool consists of five database administrators and ten network engineers. If the hiring is done without regard for the specific qualifications of the applicants, find the probability that the four hired will be (d)Three database administrators and one network engineer. Round your answer to five decimal places. The probability that three database administrators and one network engineer will be hired is

Step 1 ：An engineering company has four openings and the applicant pool consists of five database administrators and ten network engineers. If the hiring is done without regard for the specific qualifications of the applicants, we need to find the probability that the four hired will be three database administrators and one network engineer.

Step 2 ：First, we calculate the combinations of choosing 3 database administrators from 5. This can be done using the combination formula \(C(n, k) = \frac{n!}{k!(n-k)!}\), where \(n\) is the total number of items, and \(k\) is the number of items to choose. So, \(C(5, 3) = 10\).

Step 3 ：Next, we calculate the combinations of choosing 1 network engineer from 10. Using the same combination formula, we get \(C(10, 1) = 10\).

Step 4 ：Then, we calculate the total combinations of choosing 4 people from 15 (the total number of applicants). Using the combination formula, we get \(C(15, 4) = 1365\).

Step 5 ：Now, we can calculate the probability of hiring three database administrators and one network engineer. The probability \(P\) is the number of favorable outcomes divided by the total number of outcomes. So, \(P = \frac{C(5, 3) \times C(10, 1)}{C(15, 4)} = \frac{10 \times 10}{1365} = 0.07326\).

Step 6 ：Finally, we round the probability to five decimal places, getting \(\boxed{0.07326}\).