Question

a group consists of seven democrats and five republicans. four people are selected to attend a conference.
a. in how many ways can four people be selected from this group of twelve?
b. in how many ways can four republicans be selected from the five republicans?
c. find the probability that the selected group will consist of all republicans.
a. the number of ways to select four people from the group of twelve is 495.
b. the number of ways to select four republicans from the group of five republicans is 5.
c. the probability is \boxed{}.
(type an integer or a simplified fraction.)

Explanation:

Step1: Recall Probability Formula

Probability of an event = $\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$. From part (a), total outcomes (select 4 from 12) is 495. From part (b), favorable outcomes (select 4 from 5 Republicans) is 5.

Step2: Calculate Probability

Substitute into the formula: $\frac{5}{495}$. Simplify by dividing numerator and denominator by 5: $\frac{5\div5}{495\div5}=\frac{1}{99}$.

Answer:

$\frac{1}{99}$