Question 304515
In the ordinary alphabet of 26-letters. 
a) Define a "4-letter word" to be any list of 4 letters that contains at least one of the vowels A, E, I, O, U. How many 4-letter words are there?
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Assuming that repetition is not allowed:

There are 26*25*24*23 4-letter words with no restrictions.
There are 19*18*17*16 4-letter words that have no vowels.
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So, there are (26*25*24*23)-(19*18*17*16) 4-letter words that have at least one vowel.
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b) Suppose, instead, we define a "4-letter word" to be any list of 4 letters that contains exactly one of the vowels A, E, I, O, U. How many 4-letter words are there?
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5-ways to choose the vowel
19*18*17 ways to choose the other three letters
Total words = 5*19*18*17
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Cheers,
Stan H.