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How many 4-letter words with at least one consonant can be constructed from the letters A, B, C, D, E, and F? (Note that B, C, D, and F are consonants, any word is valid, not just English language words, and letters may be used more than once.)

 Oct 16, 2020
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You have 6 letters: A, B, C, D, E, F. Since they can be repeated, you will therefore have: 6^4 =1,296 permutations, or 4-letter "words". But each "word" must have at least one consonant. Therefore, we have to remove ALL 4-letter "words" that are only vowels. There are very few such permutations. Beginning with "A", there are only 8 such permutation as follows:

AAAA, AAAE, AAEA, AAEE, AEAA, AEAE, AEEA, AEEE.
Similarly, beginning with "E", there are also 8 such permutations.

 

So then, the total number of 4-letter permutations or "words" =6^4 =1,296 - 8 - 8 =1,280 such 4-letter "words"

 
 Oct 16, 2020

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