Question

A committee of seven Congressmen will be selected from a group of six democrats and nine republicans. Find the number of ways of obtaining exactly one democrat

Answer 1

The committee will be selected from = 6 republicans and 1 democrat.

Now, we can select one democrat from a group of six democrats:

6C1

Use combination formula:

`\begin{gathered} 6C1=(6!)/(1!(6-5)!) \\ 6C1=6 \end{gathered}`

Then, the number of ways to choose the republicans:

`\begin{gathered} 9C6=(9!)/(6!(9-6)!) \\ 9C6=84 \end{gathered}`

Hence, the number of ways to choose the committee consisting of 1 democrat and 6 republicans is 504 ways:

6*84 = 504 ways