APPLICATIONS

Choosing a Committee A committee of five is chosen randomly from a group of six males and eight females. What is the probability that the committee includes either all males or all females?

To find:

The probability that the committee includes either all males or all females.

Given:

There are 6 males and 8 females in the committee.

Chosen committee consists of five people.

Approach:

P(E)=n(E)n(S) …(1)

Here, P(E) is the probability of the event E.

n(E) is the number of elements in E.

n(S) is the number of elements in the sample space S.

Calculation:

Let E be the event that the committee includes all males.

The total number of people in the committee is 14

The total number of ways of selection of five people from the committee is C(14,5)

The total number of males in the committee is 6

The total number of ways of selection of five males from the committee is C(6,5)

Substitute C(6,5) for n(E) and C(14,5) for n(S) in equation (1).

P(E)=C(6,5)C(14,5)=6!5!1!14!5!9!=6!×9!14!

Now, let F be the event that the committee includes all females