Question

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

Answer 1

Answer:

39.16% probability of selecting three Democrats and three Republicans

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question, the order in which the people are selected is not important. So we use the combinations formula to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

Desired outcomes:

3 Democrats, from a set of 8.

3 Republicans, from a set of 8.

$D = C_{8,3}*C_{8,3} = (C_{8,3})^{2} = (\frac{8!}{3!5!})^{2} = 56^2 = 3136$

Total outcomes:

6 people from a set of 16.

$T = \frac{16!}{6!10!} = 8008$

Probability:

$p = \frac{D}{T} = \frac{3136}{8008} = 0.3916$

39.16% probability of selecting three Democrats and three Republicans