How many arrangements of the letters in INSTRUCTOR have all of the following properties simultaneously?
(a) The vowels appearing in alphabetical order
(b) At least 2 consonants between each vowel
(c) Begin or end with the 2 Ts (the Ts are consecutive)
We first place the vowels, IOU and there's only 1 way to do that. Then, we place TT and there's 2 ways to do that:
IOUTT or TTIOU
Now we're left with 5 consonants RRNSC. This is where I'm really having trouble with the question.
These are the possible places they can go:
_ I _ _ _ O _ _ _ U _ TT _
There must be 2 consonants between I and O and O and U. But there can't be more than 3 consonants between either I and O or O and U.
I don't know what to do from here. Do I split it into cases?