TITLE: The number of words in which the relative order of vowels and consonants remain unchanged.
QUESTION [6 upvotes]: If as many more words as possible be formed out of the letters of the word $DOGMATIC$ then compute the number of words in which the relative order of vowels and consonants remain unchanged.

Since the position of vowels and consonants is not to be changed,so the total ways are $3!\times 5!=720$
But the answer given is $719.$

REPLY [4 votes]: Yes, the answer will be $719$ because you have to find the the number of new words formed since the question says,”as many more words as possible”. $720$ is the count including DOGMATIC, therefore new words formed will be $720-1=719$.