SOLUTION: In how many ways can the letters of HEPTAGON be permuted so that the vowels are never separated?

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Question 891677: In how many ways can the letters of HEPTAGON be permuted so that the vowels are never separated?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
HEPTAGON
Example: NHEOATGP

That example has the vowel sequence EOA 

The vowels {A,E,O} can be arranged together in any of 3! ways.

For each of those 3! ways, we can form the permutation of these 6 things: 

H,P,T,G,N,(vowel sequence)

in 6! ways.

Answer: 3!6! = 6*120 = 720 ways.

Edwin