Question

HW Score: 50%, 2 of 4 point

O Points: 0 of 1
A city council consists of five Democrats and seven Republicans. If a committee of six people is selected, find the probability of selecting two Democrats and four Republicans.
Homework: Section 11.5
(Type a fraction. Simplify your answer.)
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Question 3, 11.5.13 >
CE

Answer 1

Step 1

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

Step 2

First, we have to find how many ways to choose 2 democrats from 5 which is;

`5_(c_2)`

and 4 republicans from 7 which is;

`7_(c_4)`

Then just multiply the two together to get the number of ways the two can be combined

`5_(c_2)=(5!)/(2(5-2)!)=10`
`7_(c_4)=(7!)/(4!(7-4)!)=35`

Answer;

`\begin{gathered} 5_(c_2)*7_(c_4)=10*35=350ways \\ P=(350)/(924)=(25)/(66) \end{gathered}`