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?

(In reply to solution by Charlie)

Numerically this comes out to the following for various values of n:

1 0
2 .5
3 .3333333333333333
4 .3749999999999999
5 .3666666666666668
6 .3680555555555558
7 .3678571428571427
8 .3678819444444442
9 .3678791887125222
10 .3678794642857141
11 .3678794392336056
12 .3678794413212808
13 .3678794411606918
14 .3678794411721625
15 .3678794411713976
16 .3678794411714453
17 .3678794411714414
18 .3678794411714417
19 .3678794411714417
20 .3678794411714417

Posted by Charlie on 2003-10-12 09:49:02