Question

If there are 5 boys and 7girls, in how many ways can 5 boys and 5girls sit in a round table?
Is the ans : 5!*4!*7c5?

Reason: since there are 5 boys so (5-1)!
And left 5 seats for girls so 7c5 and within the girls theres 5 diffrent ones so another 5!
Math
I forgot to add that the boys and girls need to be in alternated seats