How many ways can this be done if mom and dad sit together and the males and females alternate?

Question

Mom and dad and their 4 children (4 boys and 4 girls) are to be seated at a circular table. How many ways can this be done if mom and dad sit together and the males and females alternate?

Comments

2 boys and 2 girls make 4 children. 4 boys and 4 girls make 8 children. Which is it?

Answer 1

Assume family consists of Mom, Dad, 2 boys and 2 girls. If all genders alternate then MDGBGB fits that arrangement. So does DMBGBG. The children can be arranged B1G1B2G2, B2G1B1G2, B2G2B1G1, B1G2B2G1 and four arrangements with the genders reversed. Combined with M and D we therefore have 8 arrangements. But there are 6 seating positions around the table so in total there are 6*8=48 arrangements.

Answer 2

Können Sie es Millionen von Möglichkeiten. Ich glaube nicht, dass es eine bestimmte Zahl gibt.