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.

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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) About Me  (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:

%28matrix%282%2C1%2Cn%2Cr%29%29+=+n%21+%2F+%28r%21+%2A+%28n-r%29%21%29

So first, how many ways are there to choose two men from a group of six men? That is given by 6 choose 2:
%28matrix%282%2C1%2C6%2C2%29%29+=+15

Next, how many ways are there to choose two women from a group of five women?
%28matrix%282%2C1%2C5%2C2%29%29+=+10

Finally, how many ways are there to choose two children from four children?
%28matrix%282%2C1%2C4%2C2%29%29+=+6

Now, multiply all those together to find out how many ways there are to form the team of six people:
=
=15+%2A+10+%2A+6
=900 ways to form teams of six people given the constraints specified in the problem statement.