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 selectinga. All Republicansb. All Democrats

Answer 1

We have a total of 10 members to choose from, this means that we have a total of 10 possibilities.

a.

We have four republicans and we need to choose three of them, the number of ways to do this is:

$_4C_3=\frac{4!}{3!(4-3)!}=4$

Since we are going to choose 3 people of the total of 10 members the number of ways to do this is:

$_{10}C_3=\frac{10!}{3!(10-3)!}=120$

The probability of choosing all republicans is:

$P=\frac{4}{120}=\frac{1}{30}$

Therefore the probability is 1/30

b.

In this case we need to choose 3 people out of 3 people (since we only have 3 democrats) there's only one way to do this.

Then in this case the probability is:

$P=\frac{1}{120}$

Therefore the probability of choosing all democrats is 1/120