English has 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 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 AA, QO, XY, and UZ.)
I will answer this question, as it is actually answerable.
We can split this up into 4 cases:
CASE 1 ~ We have the variable in the front:
Since there are 6 vowels, and 20 consonants, we can multiple 6 * 20 = 120
CASE 2 ~ We have consonant in the front:
Again: 6 * 20 = 120
CASE 3 ~ Two vowels (that are the same):
Since there are 6 vowels, this will be (6 * 1) = 6
CASE 4 ~ We have 2 vowels (different):
This is 5 * 6 = 30
Add them all together, and we have: 120 * 2 + 6 + 30= 276