How many numbers are greater than 50000 can be formed with the digits 4 , 5 , 6 , 7 and 8 if no digit being repeated ?

Options

A. 96
B. 256
C. 218
D. 126

Answer

To solve the problem of how many numbers greater than 50,000 can be formed with the digits 4, 5, 6, 7, and 8 without repeating any digits, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Digits**: The available digits are 4, 5, 6, 7, and 8.

2. **Determine the Number of Digits**: Since we are looking for numbers greater than 50,000, we need to form 5-digit numbers.

3. **Identify the First Digit**: For a number to be greater than 50,000, the first digit must be either 5, 6, 7, or 8. This gives us 4 options for the first digit.

4. **Choose the Remaining Digits**: After selecting the first digit, we have 4 digits left (since no digit can be repeated). We will fill the remaining 4 positions with these digits.

5. **Calculate the Number of Arrangements**:
- For the first digit, we have 4 choices (5, 6, 7, or 8).
- For the second digit, we have 4 remaining choices (since one digit has already been used).
- For the third digit, we have 3 remaining choices.
- For the fourth digit, we have 2 remaining choices.
- For the fifth digit, we have 1 remaining choice.

6. **Multiply the Choices**: The total number of arrangements can be calculated as:
\[ \text{Total Numbers} = 4 \times 4 \times 3 \times 2 \times 1 \]

7. **Calculate the Result**:
- First, calculate \(4 \times 4 = 16\).
- Then, \(16 \times 3 = 48\).
- Next, \(48 \times 2 = 96\).
- Finally, \(96 \times 1 = 96\).

Thus, the total number of 5-digit numbers greater than 50,000 that can be formed using the digits 4, 5, 6, 7, and 8 without repeating any digits is **96**.

### Final Answer:
The total number of numbers greater than 50,000 that can be formed is **96**.