The question is:
A baby has nine different toy animals. Five of them are red and four of them are blue. She arranges them in a line so that the colours are arranged symmetrically. How many different arrangements are possible?
I understand that they key here is that they must be arranged symmetrically. Given the unequal numbers of red to blue, isn't the only arrangement possible one being B B R R R R R B B?
So shouldn't it be $4! * 5!$ ?
However, the answer is $6 *5 !* 4! $
Which combinations did I miss, or is it a more straightforward way of doing this?