Question
A family has seven children. If this family has exactly three boys, how many different birth and sex orders are possible?
There are
(Type a whole number.)
There are
(Type a whole number.)
Ask by Hill Stewart. in the United States
Mar 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
There are 35 different birth and sex orders possible.
Solution
We need to choose the positions of the three boys among the seven children. This is a combination problem where we choose 3 positions out of 7, calculated as:
Calculating further:
So, there are
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Simplify this solution Beyond the Answer
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,
So we want to calculate
Therefore, there are
