Question

A city council consists of seven Democrats and seven Republicans. If a committee of five people is​ selected, find the probability of selecting three Democrats and two Republicans.

Answer 1

Answer:

The probability of selecting three Democrats and two Republicans is 0.36

Step-by-step explanation:

Given:

The Number of Democrats = 7

The Number of Republicans = 7

To Find:

Probability of selecting three Democrats and two Republicans. = ?

Solution:  

we have to select a committee of 5 people

Now the probability of selecting three Democrats and two Republicans.

=>$\frac{\mathrm{P}(\text { Selecting three Democrats }) \cdot \mathrm{P}(\text { Selecting three Republicans })}{\mathrm{P}(\text { Selecting } 5 \text { member from total } 14)}$

=>$\frac{C(7,3) \cdot C(7,2)}{C(14,5)}$

=>$\frac{7 C_{3} \cdot 7 C_{2}}{14 C_{5}}$

=>$\frac{35\cdot 21}{2002}$

=>$\frac{735}{2002}$

=>0.36