Final answer:
There are 56 ways for a family to have 3 boys and 5 girls out of 8 children, calculated using the binomial coefficient or combinations formula C(8,3).
Step-by-step explanation:
The student's question asks about the number of ways a family can have 3 boys and 5 girls if they have 8 children in total. This is a combinatorial problem that can be solved by using the binomial coefficient, commonly referred to as "combinations."
To find the number of ways to have 3 boys and 5 girls, we can consider that the positions of the boys in the sequence of 8 children can be chosen in C(8,3) ways. We can use the formula for combinations which is:
C(n, k) = n! / (k! * (n - k)!)
Substituting n=8 and k=3, we get:
C(8, 3) = 8! / (3! * (8 - 3)!) = 8! / (3! * 5!) = (8*7*6) / (3*2*1) = 56
Therefore, there are 56 ways the family could have 3 boys and 5 girls.