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Three letters are dictated to three per...

Three letters are dictated to three persons and an envelope is addressed to each of them, the letters are inserted into the envelopes at random so that each envelope contains exactly one letter. Find the probability that at least one letter is in its proper envelope.

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To solve the problem of finding the probability that at least one letter is in its proper envelope when three letters are randomly placed into three envelopes, we can follow these steps: ### Step 1: Determine the Total Number of Arrangements We start by calculating the total number of ways to arrange the three letters into three envelopes. Since each letter can go into any envelope, the total arrangements can be calculated using the factorial of the number of letters (or envelopes). \[ \text{Total arrangements} = 3! = 6 \] ...
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