If a family has 7 children, in how many ways could the parents have 3 boys and 4 girls as children?

Question

If a family has 7 children, in how many ways could the parents have 3 boys and 4 girls as children? ​

Quizplus · Accepted Answer

The number of ways to have 3 boys and 4 girls out of 7 children is calculated using combinations, specifically $ \binom{7}{3} $ or $ \binom{7}{4} $, both of which equal 35. This is because you are choosing 3 children to be boys (or equivalently, 4 to be girls) out of 7, without regard to the order in which they are chosen.

If a Family Has 7 Children, in How Many Ways