How many ways are there to arrange the letters in the word ‘GARDEN’ with the vowels in alphabetical order ?

Solution :

Total number of ways in which all the letters can be arranged in alphabetical order = 6!

There are two vowels (A, E) in the word ‘GARDEN’.

Total number of ways in which these two vowels can be arranged = 2!

$\therefore$ Total number of required ways = $6!\over 2!$ = 360

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