The number of 4 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

Answer

To solve the problem of finding the number of 4-digit numbers that can be formed using the digits 2, 3, 4, and 7, where each digit is used only once, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Digits**: We have the digits 2, 3, 4, and 7. This gives us a total of 4 unique digits.

2. **Determine the Number of Digits to Use**: We need to form a 4-digit number, and since we have exactly 4 digits available, we will use all of them.

3. **Calculate the Number of Arrangements**: The number of ways to arrange 'n' distinct objects is given by the factorial of 'n', denoted as n!. In this case, since we have 4 digits, we need to calculate 4!.

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

4. **Conclusion**: Therefore, the total number of 4-digit numbers that can be formed using the digits 2, 3, 4, and 7, with each digit used exactly once, is 24.

### Final Answer:
The number of 4-digit numbers that can be formed is **24**.

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