In how many different ways can the letters of the word FACETIOUS be arranged in such a way that the vowels occupy only the odd positions?  Pick one:  A) 1220  B) 1860  C) 2420  D) 2880  E) 3260
The 5 vowels can be arranged in 5 odd places in 5! ways.   The 4 consonants can be arranged in 4 even places in 4! ways.   The number of arrangements with vowels in odd positions = 5! Ã— 4! = 120 Ã— 24 = 2880   The answer is 2880.
<result>D</result>
In how many different ways can the letters of the word FACETIOUS be arranged in such a way that the vowels occupy only the odd positions?