combinatorics question

The letters of the word CONSTANTINOPLE are written on 14 cards, one on each card. The cards are shuffled and then arranged in a straight line: how many arrangements are there where no two vowels are next to each other?

Can we solve it by using 9!*(14P9)
Think about placing the consonants first. How many different ways to arrange them? Then imagine inserting spaces before, between and after these consonants. How many spaces are there? How many ways to choose the spots for the vowels?