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Question

In how many ways the letters of the word "ARRANGE" can be arranged without altering the relative positions of vowels & consonants?

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Solution

VVowel , CConsonants
Given word ARRANGE is in the form VCCVCCV.
There are 4 consonants with 2 same letters (R) ξ 3 vowels with 2 same letters (A).
The vowels can be arranged in their places in 3!2! ways ξ the consonants in 4!2! ways.
Total =3!2!×4!2!=36
Hence, the answer is 36.

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