Question

(TCO 3) How many different teams can be organized consisting of two men, two women, and two children? We have the following groups available for team assignments: six men, five women, and four children. Group of answer choices 56 teams 54 teams 52 teams 58 teams

Answer 1

Answer:

900 teams

Step-by-step explanation:

The order in which the people are selected is not important(John and Josh is the same team as Josh and John), 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:

Two men(from a set of 6).

Two women(from a set of 5).

Two children(from a set of 4).

How many different teams can be organized consisting of two men, two women, and two children?

$T = C_{6,2}*C_{5,2}*C_{4,2} = \frac{6!}{2!4!}*\frac{5!}{2!3!}*\frac{4!}{2!2!} = 15*10*6 = 900$

900 teams