Dialing a telephone number an old man forgets the last two digits remambering only that these are different dialled at random. The probability that the numbe is dialled correctly, is equal to `1/k, ` then k is

Answer

To solve the problem, we need to find the probability that the old man dials the correct last two digits of the telephone number, given that he remembers that the last two digits are different.

### Step-by-Step Solution:

1. **Understanding the Problem**:
The old man has forgotten the last two digits of a telephone number. He remembers that these two digits are different. We need to calculate the probability that he dials the correct last two digits.

2. **Total Possible Combinations**:
- The last two digits can be any digit from 0 to 9. Therefore, there are 10 possible choices for the first digit and 10 choices for the second digit.
- However, since the two digits must be different, if the first digit is chosen, the second digit can only be one of the remaining 9 digits.
- Thus, the total number of combinations of the last two digits where the digits are different is:
\[ \text{Total combinations} = 10 \text{ (choices for first digit)} \times 9 \text{ (choices for second digit)} = 90. \]

3. **Successful Outcome**:
- There is only one successful outcome, which is dialing the correct last two digits.

4. **Calculating Probability**:
- The probability \( P \) of dialing the correct number is given by the formula:
\[ P = \frac{\text{Number of successful outcomes}}{\text{Total possible outcomes}} = \frac{1}{90}. \]

5. **Finding \( k \)**:
- According to the problem, the probability is given as \( \frac{1}{k} \). From our calculation, we have:
\[ \frac{1}{k} = \frac{1}{90}. \]
- Therefore, we can conclude that:
\[ k = 90. \]

### Final Answer:
Thus, the value of \( k \) is \( 90 \).