Question

How many ways are there to arrange the letters in the WORD “GARDEN ” with the vowels in alphabetical order ?

Answer 1

We found a similar question to the one that you posted. Please check it out here.

Lets first think about a situation where the order at which A and E appears doesn't matter.
We will have 6! ways in which this can be achieved. Now comes the twist. In half these arrangements possible, A will be before E and other half E will be before A.
Hence total number of ways required =6!2=360.