Three letters are written to different persons , and the addresses on the three envelopes are also written . Without looking at the addresses , find the probability that the letters go into the right envelopes .

Answer

To solve the problem of finding the probability that three letters are placed in the correct envelopes, we can follow these steps:

### Step 1: Determine the total number of outcomes
We have 3 letters and 3 envelopes. The total number of ways to arrange these letters into the envelopes is given by the factorial of the number of letters/envelopes.

\[ \text{Total outcomes} = 3! = 3 \times 2 \times 1 = 6 \]

### Step 2: Determine the number of favorable outcomes
The favorable outcome in this scenario is the situation where all letters are placed in their correct envelopes. There is only one way for this to happen, which is when each letter goes into its corresponding envelope.

\[ \text{Favorable outcomes} = 1 \]

### Step 3: Calculate the probability
The probability of an event is calculated as the ratio of the number of favorable outcomes to the total number of outcomes.

\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{1}{6} \]

### Final Answer
Thus, the probability that the letters go into the right envelopes is:

\[ \frac{1}{6} \]

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