A deck of cards contains 52 cards, including 4 aces. If you draw 5 cards at random without replacement, what is the probability that you get exactly 2 aces?
Let's reason through the problem:

1. First, calculate the total number of ways to pick 5 cards out of 52. This can be done using combinations: C(52,5) = 52! / (5!(52-5)!) = 2,598,960 possible combinations.
2. Calculate the number of ways to pick 2 aces from the 4 available aces: C(4,2) = 4! / (2!(4-2)!) = 6 possible combinations.
3. Calculate the number of ways to pick the remaining 3 non-ace cards from the 48 non-ace cards in the deck: C(48,3) = 48! / (3!(48-3)!) = 17,296 possible combinations.
4. Multiply the number of ways to pick 2 aces and the number of ways to pick 3 non-aces together: 6 * 17,296 = 103,776 desired combinations.
5. Divide the number of desired combinations by the total number of possible combinations: 103,776/2,598,960

Final answer: The probability of getting exactly 2 aces when drawing 5 cards is approximately 0.0399, or 3.99%.