49.8k views
5 votes
If a family has 8 children, in how many ways could the parents have 3 boys and 5 girls

User Karg
by
8.4k points

2 Answers

3 votes

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.

User Chkas
by
8.5k points
7 votes

Answer: It should only be one time.

Step-by-step explanation:

User Rick Kierner
by
8.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories