Respuesta :
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;
[tex]5_{c_2}[/tex]and 4 republicans from 7 which is;
[tex]7_{c_4}[/tex]Then just multiply the two together to get the number of ways the two can be combined
[tex]5_{c_2}=\frac{5!}{2(5-2)!}=10[/tex][tex]7_{c_4}=\frac{7!}{4!(7-4)!}=35[/tex]Answer;
[tex]\begin{gathered} 5_{c_2}\times7_{c_4}=10\times35=350ways \\ P=\frac{350}{924}=\frac{25}{66} \end{gathered}[/tex]