How many 3 digit numbers can be formed from the digits 1, 2 , 3, 4 and 5 assuming that repetition of the digits is allowed .

Options

A. 15
B. 13
C. 12
D. 11

Explanation

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

### Step-by-Step Solution:

1. **Identify the Digits Available**:
The digits we can use are 1, 2, 3, 4, and 5.

2. **Determine the Number of Places**:
We need to form a 3-digit number, which consists of three places: the hundreds place, the tens place, and the units place.

3. **Count the Choices for Each Place**:
Since repetition is allowed, we can choose any of the 5 digits for each of the three places:
- Hundreds place: 5 choices (1, 2, 3, 4, or 5)
- Tens place: 5 choices (1, 2, 3, 4, or 5)
- Units place: 5 choices (1, 2, 3, 4, or 5)

4. **Apply the Fundamental Principle of Counting**:
According to the fundamental principle of counting, if there are \( n \) ways to do one thing and \( m \) ways to do another, then there are \( n \times m \) ways to do both. Here, since each of the three places has 5 choices:
\[ \text{Total number of 3-digit numbers} = 5 \times 5 \times 5 \]

5. **Calculate the Total**:
\[ 5 \times 5 \times 5 = 125 \]

Thus, the total number of 3-digit numbers that can be formed is **125**.