Question: Karen has 12 cards, each written with a letter from the word PENNSYLVANIA. She picks a card at random. Without replacing she picks another card at random. Find the probability she picks two vowels.

I was sure the answer is $\frac{5}{12}\times\frac{4}{11}$ :-)

Answer: 
With Y as vowel:

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>  There are 5 vowels, picking a vowel first try gives you $\frac{5}{12}$ and then we have 11 letters and 4 vowels left, giving you $\frac{4}{11}$. Therefore, the answer would be $\frac{5}{12}\times\frac{4}{11}$, or $\frac{5}{33}$.
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Without Y as vowel:

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>  There are 4 vowels, picking a vowel first try gives you $\frac{4}{12}$, and then we will have 11 letters and 3 vowels left, giving you $\frac{3}{11}$. Therefore, the answer would be $\frac{4}{12}\times\frac{3}{11}$. or $\frac{1}{11}$.
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There are four vowels, which are E, A, I, and A, so there's $\frac{5}{12}$ chance that Karen will pick a vowel at the first try. At the second try, there will be three vowels and eleven cards left, so we multiply $\frac{5}{12}$ by $\frac{3}{11}$ and you will get $\frac{1}{11}$