1. **Problem statement:** Luisa draws 4 cards without replacement from a standard deck of 52 cards. We want to find the probability that she gets exactly 2 diamonds and 2 hearts in any order. 2. **Formula and rules:** The probability of an event is given by $$\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$$ - Total number of ways to draw 4 cards from 52 is given by combinations: $$52 \choose 4$$ - Number of favorable outcomes is the number of ways to choose 2 diamonds from 13 diamonds and 2 hearts from 13 hearts: $$\binom{13}{2} \times \binom{13}{2}$$ 3. **Calculate the probability:** $$\text{Probability} = \frac{\binom{13}{2} \times \binom{13}{2}}{\binom{52}{4}}$$ 4. **Explanation:** - We use combinations because the order of cards does not matter. - We multiply the combinations for diamonds and hearts because these are independent choices. - The denominator counts all possible 4-card draws from the deck. 5. **Final answer:** $$\boxed{\frac{\binom{13}{2} \times \binom{13}{2}}{\binom{52}{4}}}$$ This corresponds to option D.