How many 3-digit numbers can be formed from the digits 1,2,3,4 and 5 assuming that repetition of the digits is not allowed?

Options

A. a. 68
B. b. 130
C. c. 60
D. d. none of these

Answer

To find out how many 3-digit numbers can be formed from the digits 1, 2, 3, 4, and 5 without allowing repetition of the digits, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Total Digits Available**:
We have 5 digits available: 1, 2, 3, 4, and 5.

2. **Determine the Choices for Each Digit Place**:
- For the **hundreds place**, we can choose any of the 5 digits (1, 2, 3, 4, or 5).
**Choices for hundreds place = 5**.

3. **Choose the Digit for the Tens Place**:
After selecting a digit for the hundreds place, we cannot use that digit again (since repetition is not allowed). Therefore, we have 4 remaining digits to choose from for the tens place.
**Choices for tens place = 4**.

4. **Choose the Digit for the Units Place**:
After selecting digits for the hundreds and tens places, we have 3 digits left to choose from for the units place.
**Choices for units place = 3**.

5. **Calculate the Total Number of Combinations**:
To find the total number of different 3-digit numbers, we multiply the number of choices for each digit place together:
\[ \text{Total combinations} = (\text{Choices for hundreds}) \times (\text{Choices for tens}) \times (\text{Choices for units}) \]
\[ \text{Total combinations} = 5 \times 4 \times 3 = 60 \]

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

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