2006 SMT/General Problems/Problem 3
Problem
After a typist has written ten letters and had addressed the ten corresponding envelopes, a careless mailing clerk inserted the letters in the envelopes at random, one letter per envelope. What is the probability that exactly nine letters were inserted in the proper envelopes?
Solution
For a letter to be in the wrong envelope, another letter must also be out of its correct envelope, so it is not possible to have exactly nine in the correct envelopes. Therefore, the answer is 
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