How many 4-letter words with at least one consonant can be constructed from the letters A B C D and E? It does not have to be a word in the English language and letters may repeat.

Question

anonymous · Answer

Do they have to be words or can we use

CDBA

anonymous · Answer

they don't have to be actual words. CDBA works

across · Answer

1. You need a 4-letter word.
2. You have 5 letters to choose from.
3. The word has to have at least 1 consonant.
4. The letters can repeat, and the word doesn't have to make sense.

Well, you have 4 spaces as such:

_ _ _ _

and 5 letters: A, B, C, D and E.

The possibilities of letters one can obtain in the first space are 5. The same is the case for all other spaces. Therefore, the total number of words one could come up with are 5^4.

However, since the word has to have at least one consonant, that means that a word having all vowels would not suffice. Thus, we calculate that the number of words, without consonants, that we can come up with are 2^4.

Finally, we conclude that we can come up with a total of 5^4 - 2^4 words which fit our criteria.