A city council consists of 9 members. Four are Republicans, three are Democrats, and two are Independents. If a committee of three is to be selected, find the probability of selecting
(a)All Republicans. Round your answer to five decimal places.
The probability of selecting all Republicans is

Step 1 ：The city council consists of 9 members: 4 Republicans, 3 Democrats, and 2 Independents.

Step 2 ：We are to select a committee of 3 members.

Step 3 ：We want to find the probability of selecting all Republicans.

Step 4 ：We can calculate this using the combination formula.

Step 5 ：The total number of ways to select 3 members out of 9 is given by the combination formula C(9,3), which equals 84.

Step 6 ：The number of ways to select 3 Republicans out of 4 is given by C(4,3), which equals 4.

Step 7 ：The probability is then given by the ratio of these two quantities, which is \(\frac{4}{84} = 0.047619047619047616\).

Step 8 ：Rounding this to five decimal places, we get \(0.04762\).

Step 9 ：Final Answer: The probability of selecting all Republicans is \(\boxed{0.04762}\).