SOLUTION: In how many different ways can the letters of the word 'QUESTION' be arranged in such a way that the vowels occupy only the even positions?

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Question 928822:
In how many different ways can the letters of the word 'QUESTION' be arranged in such a way that the vowels occupy only the even positions?
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
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There are 4! ways to arrange the 4 consonants in the 4 odd positions.
For each of those 4! ways to arrange the consonants,
there are 4! ways to arrange the 4 vowels in the 4 even positions.

Answer 4!×4! = 24×24 = 576 ways.

Edwin
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