That was not in your original question, and clarifies one issue. The other big issue is, how many flowers are to be in the arrangement? It would appear that it can be any number (up to 9). Taking it this way, I get 256, assuming the flowers are distinguishable.
If they are not, then you have either 3, 4, or 5 white flowers, and either 0, 1, 2, 3, or 4 red, giving 3*5=15 ways.
You're saying that this comes from a book, which gives the answer as 81? (And not that somebody you can't trust gave that answer?)
On the whole, it's just a very poorly worded problem, or else their answer is wrong, or both. Can you just skip it?