A family has seven children. If this family has exactly three boys, how many different birth and sex orders are possible?
There are different birth and sex orders possible.
(Type a whole number.)

To find the number of different birth and sex orders for a family with seven children, where exactly three are boys (B) and four are girls (G), we can use combinations. The total arrangements of the children can be calculated using the binomial coefficient, which is given by the formula:

In this case, (the total number of children), and (the number of boys).

So we want to calculate :

Therefore, there are different birth and sex orders possible for the children.