Question 614919
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:


{{{(matrix(2,1,n,r)) = n! / (r! * (n-r)!)}}}


So first, how many ways are there to choose two men from a group of six men? That is given by 6 choose 2:
{{{(matrix(2,1,6,2)) = 15}}}


Next, how many ways are there to choose two women from a group of five women?
{{{(matrix(2,1,5,2)) = 10}}}


Finally, how many ways are there to choose two children from four children?
{{{(matrix(2,1,4,2)) = 6}}}


Now, multiply all those together to find out how many ways there are to form the team of six people:

={{{(matrix(2,1,6,2)) * (matrix(2,1,5,2)) * (matrix(2,1,4,2))}}}

={{{15 * 10 * 6}}}

=900 ways to form teams of six people given the constraints specified in the problem statement.