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

How many ways are there to arrange the letters in the word GARDEN with the vowels in alphabetical order?
  1. 120
  2. 480
  3. 360
  4. 240

Solution

Since in half the arrangement $A$ will be before $E$ and other half $E$ will be before $A$. Hence total number of ways $=\frac{6 !}{2}=360$.

Asked in: JEE Main 2004

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