Based on real life experience, I just considered the following combinatorial challenge:
In a workplace with currently $n$ employees each employee has its own unique 4-digit code used to pass through certain doors at certain times of day. Tomorrow $r$ new employees will start working there and each must fill in a form suggesting two different 4-digit codes. They have no knowledge of each others codes or the $n$ current employee's codes. When everyone has filed their forms, it is attempted to assign each new employee one of their suggested codes so that all $n+r$ persons working there have unique codes.
For simplicity, let us assume that the new employees choose their two different 4-digit suggestions uniformly at random. Then what is the probability $P(n,r)$ that the workplace is unable to assign unique codes to all the new employees?