I'm asked the following two questions: How many Strings of 6 letters contain
a) Exactly one Vowel
b) At least one Vowel
a) This is what I know: The English alphabet has 21 consonants and 5 vowels. So we choose one of those vowels as such:
$6\choose1$$5\choose1$$21\choose1$$^5$, shouldn't this give me my answer? I'm not exactly sure how to wrap my head around such questions, the answer I'm given is : 122523030
Any help would be much appreciative.