Typical permutation

Algebra Level pending

The number of different permutations of all the letters of the word PERMUTATION such that any two consecutive letters in the arrangement are neither both vowels nor both identical is
NOTE : options are in the form 63 multiplied by 6!5!.
8 multiplied by 6! 6!. 57 multiplied by 5!5!. 7 multiplied by 7!5!.

63 6! 5! 8 6! 5! 57 5! 5! 7 7! 5!

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