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

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

AIEEEAIEEE 2004Permutations and Combinations

Solution:

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