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English has 6 letters that can be vowels. This includes Y, which can be either a consonant or a vowel; for this problem, we'll consider Y a vowel.

The other 20 English letters are always consonants.

How many three-letter "words" can we make from these letters if we are required to use at least one vowel? (We aren't limited to words that have an actual meaning in English. Thus, for this problem, we'll include nonsense "words" like QOP, XYZ, and UTZ.)

 Jan 30, 2022
 #1
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20 consonants, 6 vowels,

3 letter words, at least one vowel

 

All letters different     6*25*24*3! = 900

2 vowels the same    6*25*3       = 450

2 consonants the same 6*20*3  =  360

all three the same       6             =  6

 

900+450+360+6 = 1716

 

 

Feel free to aks questions.

 Jan 30, 2022

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