Solve the problem.
-Mr. and Mrs. Smith are planning to have 5 children. How many ways can they have 3 boys and 2 girls?
A) 10
B) 60
C) 12
D) 6

Question

Quizplus · Accepted Answer

The number of ways to have 3 boys and 2 girls out of 5 children is calculated using the combination formula, which is $\binom{n}{r} = \frac{n!}{r!(n-r)!}$. Here, $n=5$ (total number of children) and $r=3$ (number of boys or alternatively, number of girls, since the question is symmetric with respect to gender). Thus, the calculation is $\binom{5}{3} = \frac{5!}{3!2!} = 10$. This represents the number of ways to choose 3 children to be boys (and the remaining 2 automatically being girls), or vice versa.

Solve the Problem. -Mr. and Mrs. Smith Are Planning to Have 5 Children