How many 4-letter words with at least one vowel can be constructed from the letters A, B, C, D, E, and F? (Note that A and E are vowels, any word is valid, not just English language words, and letters may be used more than once.)
To answer this question, you just need to subtract the number of words without vowels from the total number of words.
The total number of words is 6*6*6*6=1296
The total number of words without vowels is 4*4*4*4 = 256
Therefore, the answer to this question is 1296-256=1040 words.