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

Options

A. `1//27`
B. `1//6`
C. `1//9`
D. none of these

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: Understand the total arrangements
We have 3 letters and 3 envelopes. The total number of ways to arrange the letters in the envelopes is given by the factorial of the number of letters (or envelopes), which is \(3!\).

\[ 3! = 3 \times 2 \times 1 = 6 \]

### Step 2: Identify the favorable outcomes
There is only one favorable outcome where all three letters are placed in their correct envelopes. This means that there is only 1 way for the letters to be arranged correctly.

### Step 3: Calculate the probability
The probability \(P\) that all letters go into the correct envelopes is given by the ratio of the number of favorable outcomes to the total number of outcomes.

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

Thus, the probability that the letters go into the right envelopes is \(\frac{1}{6}\).

### Final Answer
The probability that the letters go into the right envelopes is \(\frac{1}{6}\).

---