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=(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=(10!)/(3!(10-3)!)=120`

The probability of choosing all republicans is:

`P=(4)/(120)=(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=(1)/(120)`

Therefore the probability of choosing all democrats is 1/120