1, 2, 3, 4 are four numbers. How many numbers can be made using all four numbers without repetition?

Options

A. 1!
B. 3!
C. 2!
D. 4!

Answer

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

### Step 1: Identify the total digits
We have four distinct digits: 1, 2, 3, and 4.

### Step 2: Determine the number of choices for each digit
- For the **first digit**, we can choose any of the 4 digits (1, 2, 3, or 4). So, there are **4 choices**.
- For the **second digit**, since we cannot repeat the digit used in the first position, we have **3 remaining choices**.
- For the **third digit**, we will have **2 choices** left after selecting the first two digits.
- For the **fourth digit**, there will be **1 choice** remaining after selecting the first three digits.

### Step 3: Calculate the total arrangements
To find the total number of arrangements, we multiply the number of choices for each digit:
\[ \text{Total arrangements} = 4 \times 3 \times 2 \times 1 \]

### Step 4: Simplify the expression
This can be simplified as:
\[ 4 \times 3 \times 2 \times 1 = 24 \]

### Step 5: Conclusion
Thus, the total number of different numbers that can be formed using all four digits without repetition is **24**.

### Final Answer
The answer is **24**.

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