A student-faculty government committee of 4 people is to be formed from 23 student volunteers and 5 faculty volunteers. Find the probability that the committee will consist of the following, assuming the selection is made at random:
(d)One faculty member and three students. Round your answer to five decimal places.

The probability that the committee will consist of one faculty member and three students is

Step 1 ：We are given 23 student volunteers and 5 faculty volunteers, a total of 28 people. We want to form a committee of 4 people.

Step 2 ：The total number of ways to form a committee of 4 people from 28 is given by the combination formula \(C(n, k) = \frac{n!}{k!(n-k)!}\), where n is the total number of people and k is the number of people to choose. In this case, n = 28 and k = 4. So, the total number of ways is \(C(28, 4) = 20475\).

Step 3 ：The number of ways to choose 1 faculty member from 5 is \(C(5, 1) = 5\), and the number of ways to choose 3 students from 23 is \(C(23, 3) = 1771\).

Step 4 ：The probability that the committee will consist of one faculty member and three students is given by the ratio of the number of favorable outcomes (one faculty member and three students) to the total number of outcomes (any committee of 4 people). So, the probability is \(\frac{5 \times 1771}{20475} = 0.4324786324786325\).

Step 5 ：Rounding to five decimal places, the final answer is \(\boxed{0.43248}\).