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.)

Darkside
Sep 2, 2018

#1**+2 **

There are \(5\) letters to choose from and \(4\) letters make up a word. We can get the permutation _{5}P_{4} = \(120\).

- Daisy

dierdurst
Sep 2, 2018

#3**+1 **

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.)

Daisy's answer would be correct if the letters could only be used once.

How many 4 letter words can be constructed from ABCDE that would be 5^4 = 625

How many 4 letter words can be constructed using BCD that would be 3^4 = 81

So the number of words that use at least one vowel would be 5^4 - 3^4 = 625-81 = **544 **

Melody
Sep 3, 2018