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 two-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 QO, XY, and UZ.)

SmartMathMan  Jan 11, 2018

We can use any vowel  = 6 choices and any consonant  = 20 choices


And the vowel can come first or the consonant can come first  =  2 choices


So.....with one vowel we have  6 * 20 * 2  =  240 "words"



We can also use   a word with the same vowel repeated = 6 "words"


We can  also select any one of the vowels first  = 6 choices  and any one of the remaining vowels second  = 6 * 5  = 30 "words"


So......   240 +  6  +  30    =    276 "words"




cool cool cool

CPhill  Jan 11, 2018

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