1. The problem statement, all variables and given/known data Suppose we have two decks with n distinct cards each. After we shuffle the decks, what is the probability that k cards are in the same position in the two decks? 2. Relevant equations 3. The attempt at a solution I have worked out that when n tends to infinity, the probability that 0 cards are in the same position is 1/e but I am having a lot of difficulties with the combinatorics aspect of the problem. Hope you guys could help me with that! Thanks!