You can put this solution on YOUR website! Ans:
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There are only two vowels, e and i. So for words ending in 'i' you have 4!= 24 permutations of the remaining 4 letters, and similarly 4!=24 for words ending in 'e'. Adding these gives 48.
( Since this is a MATH forum it is understood that a 'word' is a unique sequence of letters, and not necessarily a word from, say, a dictionary. )