The number of different four - digit numbers that can be formed with the digits 2, 3, 4, 7 and using each digit only once is

Options

A. 120
B. 96
C. 24
D. 100

Explanation

To find the number of different four-digit numbers that can be formed using the digits 2, 3, 4, and 7, with each digit used only once, we can follow these steps:

### Step 1: Identify the Digits
The digits we have are 2, 3, 4, and 7. We need to form a four-digit number using all of these digits.

### Step 2: Determine the Number of Choices for Each Position
Since we are forming a four-digit number, we will fill four positions (thousands, hundreds, tens, and units) with the available digits.

- For the **first position** (thousands place), we can choose any of the 4 digits (2, 3, 4, 7). So, we have **4 choices**.
- For the **second position** (hundreds place), we can choose from the remaining 3 digits (since one digit has already been used in the first position). So, we have **3 choices**.
- For the **third position** (tens place), we can choose from the remaining 2 digits. So, we have **2 choices**.
- For the **fourth position** (units place), only 1 digit will be left. So, we have **1 choice**.

### Step 3: Calculate the Total Number of Combinations
The total number of different four-digit numbers can be calculated by multiplying the number of choices for each position:

\[ \text{Total combinations} = 4 \times 3 \times 2 \times 1 \]

### Step 4: Perform the Calculation
Now, we perform the multiplication:

\[ 4 \times 3 = 12 \]
\[ 12 \times 2 = 24 \]
\[ 24 \times 1 = 24 \]

Thus, the total number of different four-digit numbers that can be formed is **24**.

### Final Answer
The number of different four-digit numbers that can be formed with the digits 2, 3, 4, and 7, using each digit only once, is **24**.

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