MHB Combinatorics: Solve No Vowel Arrangement

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To solve the problem of arranging the letters in "CONSTANTINOPLE" with no two vowels adjacent, first identify the vowels (O, A, I, O, E) and consonants (C, N, S, T, N, T, N, P, L). There are 5 vowels and 9 consonants. Arrange the consonants first, which can be done in 9!/(3!2!) ways due to repetitions. After placing the consonants, there are 10 possible slots for the vowels, and the vowels can be arranged in those slots in 5!/(2!) ways. The total number of arrangements is the product of the two calculations.
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please help solving this 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?
 
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