The letter of the word CONSTANTINOPLE are written on 14cards, one on each card. the cards are shuffled and then arranged in a straight line.

(d) How many arrangements are there when no two vowels are next to each other?

There are 5 vowels here as I see it, A, I, E, 2 x O.

If we let vowels = V and consonants = C, then an arrangement like this can happen:

We have (14 - 5) = 9 consonants

- C1 - C2 - C3 - C4 - C5 - C6 - C7 - C8 - C9 -

Now, we have 10 places to input the first vowel, 9 for 2nd, 8 for 3rd, 7 for 4th, 6 for 5th ...

I am not sure how to solve it next. I did (9! / (3! 2!)) x 10 x 9 x 8 x 7 x 6 but that doesn't work and I am not sure what am I doing wrong.