Selecting a committee

Question

A city council consist of 8 Democrats and 5 Republicans. If a committee of 6 people is selected, find the probability of selecting 4 Democrats and 2 Republicans.

Answer 1

Mike,

        The number of ways of choosing 4 dems out of 8 is ₈C₄=70

        The number of ways of choosing 2 reps out of 5 is  ₅C₂=10

 

So the number of different 6 person committees having 4 dems and 2 repubs is 70*10=700

The total number of 6 person committees out of 13 people is ₁₃C₆=1716

Using the definition of probability P(4dem and 2repub)=700/1716=.408

 

Hope this helps

Jim

 

Answer 2

There are 13 people.

The number of ways of selecting a group of 6 out of this 13 is 13C6 = X

The number of ways of selecting 4 Democrats from 8 Democrat = 8C4 = Y

The number of ways of selecting 2 Republicans from 5 Republicans = 5C2 = Z

 

The probability of selecting 4 Democrats and 2 Republicans = YZ/X

 

Use a calculator or otherwise, to solve for X, Y, and Z. Then find YZ/X.