chris, can you explain more.
what's the difference with, "in how many ways can the word 'mobile' be rearanged to form 6 letter words such that the vowels take odd positions"?
in the mobile thing, it's 3! * 3!
why don't we apply the same thing to 'double' and then subtract 3!.
I guess am missing a piece of the logic!
in the question with the word double, you have 6 spaces _ _ _ _ _ _ . you can place the vowels in much more places as you can place them in the question about the word mobile. o u e _ _ _ or o _ u e _ _ or _ _ ou _ e and so on.its only important that the order is o u e. in the second question you have again 6 spaces and you can place the vowels only on the odd positions. so its o _ i _ e _. the main difference is that in the 2nd quest., you have only 1 way to place the letters with different letters and in the 1st question, there are many ways with different letters. by the way in the double-question you divide by 3! because otherwise o u e as well as e o u would be counted, but ONLY o u e is permitted and so you divide by 3! to get rid of these arrangements.
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