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Probability of Envelopes

I need assistance with following problem along with steps to arrive at the solution/answer.

Three envelopes are addressed for 3 secret letters written in invisible ink. A secretary randomly places each of the letters in an envelope and mails them. What is the probability that at least 1 person receives the correct letter?

Solution This solution is FREE courtesy of BrainMass!

Suppose 3 envelopes are denoted as A, B, C and the 3 secret letters are denoted as a, b, c. They should be put in envelopes A,B,C, respectively. It means a-A, b-B, c-C is the only way for all the people to receive the correct letter.

If the secretary randomly places each of the letters in an envelope, there are 3!=6 different choices. Only 2 cases make nobody receive the correct letter. The 2 cases are: a-B, b-C, c-A and a-C, c-B, b-A. For the other 4 cases, at least 1 person can receive the correct letter.

Therefore, the probability is 4/6=2/3.