A student-faculty government committee of 4 people is to be formed from 18 student volunteers and 6 faculty volunteers. Find the probability that the committee will consist of the following, assuming the selection is made at random:
Part: 0 / 4
Part 1 of 4
(a) All faculty members. Round your answer to five decimal places.
The probability that the committee will consist of all faculty members is
Answer
Final Answer: The probability that the committee will consist of all faculty members is \(\boxed{0.00141}\).
Step 1 ：The total number of ways to form a committee of 4 people from 24 people (18 students + 6 faculty) 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 in the committee. In this case, n = 24 and k = 4. So, the total number of ways is 10626.
Step 2 ：The number of ways to form a committee of 4 faculty members from 6 faculty members is also given by the combination formula. In this case, n = 6 and k = 4. So, the number of ways to form a committee of 4 faculty members is 15.
Step 3 ：The probability that the committee will consist of all faculty members is then given by the ratio of the number of ways to form a committee of 4 faculty members to the total number of ways to form a committee of 4 people. So, the probability is \(\frac{15}{10626} = 0.001411631846414455\).
Step 4 ：Final Answer: The probability that the committee will consist of all faculty members is \(\boxed{0.00141}\).
