SOLUTION: How many different teams can be organized consisting of 2 men, 2 women and 2 children? We have the following groups available for team assignments: 6 men, 5 women and 4 children.

Question 614919: How many different teams can be organized consisting of 2 men, 2 women and 2 children? We have the following groups available for team assignments: 6 men, 5 women and 4 children.
Answer by ashipm01(26) (Show Source): You can put this solution on YOUR website!
If you have n elements in a set and you need to choose r elements from that set, there are n choose r ways of doing that. The following function calculates the number of ways to choose r elements from an n element set:

So first, how many ways are there to choose two men from a group of six men? That is given by 6 choose 2:

Next, how many ways are there to choose two women from a group of five women?

Finally, how many ways are there to choose two children from four children?

Now, multiply all those together to find out how many ways there are to form the team of six people:
=
=
=900 ways to form teams of six people given the constraints specified in the problem statement.
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