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

Answer:

319,770 different task force groups might possibly be formed

Step-by-step 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.

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

In this question:

Groups of 8 from a set of 22. So

$C_{22,8} = \frac{22!}{8!(22-8)!} = 319770$

319,770 different task force groups might possibly be formed