Yes I understand that. But again you are referring to all the boys as b or 1 or whatever and all the girls as g or 0.
My contention is that given an ordering you can label the boys b1 b2 b3 and the girls g1 g2 and when this is done the sequence
b1 b2 b3 g1 g2 is not the same as the sequence b2 b1 b3 g1 g2
I'm going to leave it at this point. If you all say the question implies the children are indistinguishable other than gender I'll take your word for it.