How many 3-digit numbers can be formed by using 1, 2, 3, 4, 5 without repetition of digits?

Options

A. 12
B. 22
C. 50
D. 60

Answer

To solve the problem of how many 3-digit numbers can be formed using the digits 1, 2, 3, 4, and 5 without repetition, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Total Digits Available**:
We have the digits 1, 2, 3, 4, and 5. This gives us a total of 5 different digits to choose from.

2. **Choose the First Digit**:
For the first digit of the 3-digit number, we can choose any of the 5 digits.
- **Choices for the first digit**: 5 options (1, 2, 3, 4, or 5).

3. **Choose the Second Digit**:
After selecting the first digit, we cannot use that digit again (since repetition is not allowed). Therefore, we have 4 remaining digits to choose from for the second digit.
- **Choices for the second digit**: 4 options (remaining digits after the first choice).

4. **Choose the Third Digit**:
After selecting the first and second digits, we again cannot use those digits. This leaves us with 3 remaining digits to choose from for the third digit.
- **Choices for the third digit**: 3 options (remaining digits after the first and second choices).

5. **Calculate the Total Combinations**:
To find the total number of different 3-digit combinations, we multiply the number of choices for each digit position together:
\[ \text{Total combinations} = 5 \times 4 \times 3 \]

6. **Perform the Calculation**:
\[ 5 \times 4 = 20 \]
\[ 20 \times 3 = 60 \]

7. **Conclusion**:
Therefore, the total number of 3-digit numbers that can be formed using the digits 1, 2, 3, 4, and 5 without repetition is **60**.

### Final Answer:
The total number of 3-digit numbers that can be formed is **60**.

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