Question

A membership committee for a local community group consists of twenty-two individuals. a. If a task force of eight members of this committee must be formed to investigate the membership rules, how many different task force groups might possibly be formed

Answer 1

319,770 different task force groups might possibly be formed

Explanation:

The order in which the members of the task force are chosen is not important, which means that the combinations formula is used 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) = (n!)/(x!(n-x)!)`

In this question:

Groups of 8 from a set of 22. So

`C_(22,8) = (22!)/(8!(22-8)!) = 319770`

319,770 different task force groups might possibly be formed