Consider the layout of the letters given your constraints. You have 3 vowels and 7 consonants. Using 'a' to represent any vowel and 'X' to represent any consonant we have:
Then think about possible ways to arrange the different vowels and consonants in those layouts. Watch out for the double T and double R.
EDIT: a bit more generally to think about how to generate the layouts consider this. There are 3 vowels and 7 consonants. The vowels act like gaps between the consonants so there are 2 places which must have 2 consonants. That leaves 3 consonants to place.