(adsbygoogle = window.adsbygoogle || []).push({}); 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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Forming pairs problem

**Physics Forums | Science Articles, Homework Help, Discussion**