There are 10 students in a class, 5 boys and 5 girls. how many ways can i sit them around a harkness table? explain well because i'm confused

I will take a go at this. Imagine you had 10 chairs to put people in, and you had 10 people. For the first chair, you can pick out of 10 people, for the second chair, you have 9 people to pick from, and so on until the last chair, where you don't have a choice. So, to find the possible ways you can sit people in the chairs, you do 10*9*8*7*6*5*4*3*2*1, or you can denote it as 10!, where ! means factorial. So you get 3628800, and at first you might think that would be the answer, but we are talking about a circular arrangement here. So, two arrangements would be counted as different just because it turns by one person (Shown in picture). So since we dont count the first one, it should just be 9! instead of 10! And 9! equals 362880 (One less zero than the other answer). That should be the right answer

english, cause i can’t you