1. The problem statement, all variables and given/known data 4 cards are dealt from a 52-card deck. How many hands contain 2 distinct pairs? 2. Relevant equations This is an expression I come up with 13C1x4C2x12C1x4C2. 3. The attempt at a solution This is how I approach it. From the 13 ranks, I choose 1. In this rank, I choose 2 cards from 4. From the remaining 12 ranks, I choose 1. In this rank, I choose 2 cards from 4. Now, I do the following calculations with combinations. 13C1x4C2x12C1x4C2 = 5616. My neighbor told me that it's wrong. He didn't explain why it was wrong. I cannot find any mistakes. Please explain what I have done wrong. Thank you very much.