How many 2- digits numbers can be formed from the digits 8,1,3,5 and 4 assuming
repetition of digits is allowed?

Answer

To solve the problem of how many 2-digit numbers can be formed from the digits 8, 1, 3, 5, and 4 with repetition allowed, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Digits**: The digits available for forming the numbers are 8, 1, 3, 5, and 4. This gives us a total of 5 digits.

2. **Determine the Structure of a 2-Digit Number**: A 2-digit number consists of two places: the tens place and the units place.

3. **Calculate Choices for Each Place**:
- For the **tens place**, since repetition is allowed, we can choose any of the 5 digits (8, 1, 3, 5, 4). Therefore, there are 5 choices for the tens place.
- For the **units place**, again, since repetition is allowed, we can also choose any of the 5 digits. Thus, there are also 5 choices for the units place.

4. **Calculate the Total Number of 2-Digit Numbers**:
- The total number of 2-digit numbers can be calculated by multiplying the number of choices for the tens place by the number of choices for the units place:
\[ \text{Total 2-digit numbers} = \text{Choices for tens place} \times \text{Choices for units place} = 5 \times 5 = 25. \]

5. **Conclusion**: Therefore, the total number of 2-digit numbers that can be formed from the given digits with repetition allowed is **25**.