Suppose there are n people in an office. At Christmas they have a random gift exchange in which every name is writen on scraps of paper, mixed around in a hat, and then everyone draws a name at random to determine who they are to get a gift for.

What is the probability nobody draws their own name?

We do a pressie dip each Christmas at our office and have had this problem on occasions. My solution is ((n-1)/n))^(n-1) as each person has a (n-1)/n chance of not picking their own except the last person who has 100% chance. The probability for each person remains the same as there is a chance that their name has already been removed by the earlier pickers. For high n this does come out close to the other solution. The case for n=3 is interesting as my answer gives 0.4444 - not 0.3333. I may sit with some bits of paper over Christmas to test this....

Posted by Jils on 2003-12-17 04:33:48