Problem 75 Answer

The answer is 1/2! - 1/3! + 1/4! - 1/5! ... +/- 1/n!.

Here are some approxmiate probabilities for number of people n:

n       Prob(no matches)
--      ----------
2	50.000000%
3	33.333333%
4	37.500000%
5	36.666667%
6	36.805556%
7	36.785714%
8	36.788194%
9	36.787919%
10	36.787946%
11	36.787944%
12	36.787944%
13	36.787944%
14	36.787944%
15	36.787944%
Note that the probabilities quickly converge to 1/e.

Michael Shackleford, A.S.A.