I have a query about this question:
Five boys and five girls are to sit around a table. Find in how many ways this can be done if the boys and girls alternate.
I know this question has been asked before, but I really don't understand why my specific solution is incorrect.
I thought that the answer would be $4!5!*2$, because you take the case that the initial person being seated is a boy, which has $4!5!$ permutations, then you multiply by $2$ to take into account the permutations, for which a girl is initially seated.