In how many ways can 4 boys and 4 girls sit around a circle table if each boy sits between two girls? (Rotations of the same arrangement are still considered the same. Each boy and girl is unique, not interchangeable.)
I said that it has to be of the form BGBGBGBG, so there would be (4!)(4!) ways to order the boys and the girls. However, you have to divide by 8 for overcounting, because there are 8 ways to rotate any order. This would be 576/8=72 ways. However, this is wrong. Could I get some help? Thank you.