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I'm not sure, but i have there are 26x25x24x23 total possibilities which is 358800. And 21x20x19x18 of these possibilities don't include vowels (since 21 out of 26 letters are not vowels and they can each be used once). Therefore the number of possibilities of words WITH vowels is just the difference which is 358800 - 143640 = 215160

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Q: How many four letter words can you make if no letter is used twice and each word must contain at least one vowel?
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