### Instruction: How many 4-letter words with at least one vowel can be constructed from the letters A, B, C, D, and E?  (Note that A and E are vowels, any word is valid, not just English language words, and letters may be used more than once.).### Response: I need to count how many words I can make with these letters, and then subtract the ones that have no vowels at all.
To make a word with these letters, I have 5 choices for the first letter, 5 for the second, 5 for the third, and 5 for the fourth. So, the total number of words is 5^4 = 625.
Now, how many of these have no vowels?
Well, that means I can only use B, C, and D for each letter. So, the number of words with no vowels is 3^4 = 81.