How many 4-letter words with at least one consonant can be constructed from the letters a, B,C,D , and E? (Note that b,c , and d are consonants, any word is valid, not just English language words, and letters may be used more than once.)
Assuming that we can have "non-sense" words
We could have a word with an "A" and this letter could appear in any of 4 positions......and we could choose any of the other three consonants to occupy a second positon, then any two of the consonants to occupy a third position, and the last consonant would appear in the last position by default.......so we have
4 * 3 * 2 *1 = 24 words using just the A and the other three consonants
The same result would occur if we just used the "E" and the other three consonants
If we used the "A" and the "E," we would have 24 words using any two of the other consonants......but, we could choose any 2 of the 3 remaining consonants.....so the total "words" would be 24 * (3C2) = 24 * 3 = 72
So....the total number of words would be 24 + 24 + 72 = 120 "words"