Question

a city council consists of 10 members. four are republicans, three are democrats, and three are independents. if a committee of three is to be selected, find the probability of selecting
part 1 of 5
(a) all republicans. round your answer to five decimal places.
the probability of selecting all republicans is 0.03333.
part 1 / 5
part 2 of 5
(b) all democrats. round your answer to five decimal places.
the probability of selecting all democrats is

Explanation:

Step1: Calculate the combination

The formula for combination is \(C(n,k)=\frac{n!}{k!(n - k)!}\), where \(n\) is the total number of items, and \(k\) is the number of items to be chosen.
The total number of ways to select a committee of \(3\) from \(10\) members is \(C(10,3)=\frac{10!}{3!(10 - 3)!}=\frac{10\times9\times8}{3\times2\times1}=120\).
The number of Democrats is \(3\). The number of ways to select \(3\) Democrats from \(3\) Democrats is \(C(3,3)=\frac{3!}{3!(3 - 3)!}=1\).

Step2: Calculate the probability

The probability \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\).
Substitute the values: \(P=\frac{C(3,3)}{C(10,3)}=\frac{1}{120}\approx0.00833\)

Answer:

\(0.00833\)