How many 3-letter "words" can be formed from the standard 26-letter alphabet, if the first letter must be a vowel (A, E, I, O, or U)? (We aren't necessarily talking about English words; something like EQX is perfectly valid here.)
I need to count the number of ways to choose a vowel for the first letter, then any letter for the second and third letters. For the first letter, I have 5 choices: A, E, I, O, or U. For the second letter, I have 26 choices, since I can use any letter of the alphabet. For the third letter, I also have 26 choices, for the same reason. So, the total number of 3-letter "words" is 5 times 26 times 26, which is 5 times 676, which is 3380. 