Singapore Math 6th grade probability problem 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 $\frac{5}{12}\times\frac{4}{11}$ :-)

With Y as vowel:

 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 $\frac{5}{33}$.

Without Y as vowel:

 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 $\frac{1}{11}$.

