Question

A city council consists of five Democrats and six Republicans. If a committee of six people is selected, find the probability of selecting four Democrats and twoRepublicans

Answer 1

Given:

The number of democrats = 5.

The number of republicans = 6.

Aim:

We need to find the probability of selecting four Democrats and two Republicans.

Explantion:

The possible way to select four Democrats

`=5C_4=5`

The possible way to select 2 republicans is

`=6C_2=15`

The total way to select 6 people is

`=11C_6=462`

The probability of selecting four Democrats and two Republicans is

`=(5C_4\cdot6C_2)/(11C_6)`

`=(5*15)/(462)`

`=(75)/(462)=(25)/(154)`

The probability of selecting four Democrats and two Republicans is 25/154.

Final answer:

The probability of selecting four Democrats and two Republicans is 25/154.