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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.

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