How many number can be formed by using digits 0,2,4,6,8 greater then 10000 where repetition of digits are not allowed

Answer

To solve the problem of how many numbers greater than 10,000 can be formed using the digits 0, 2, 4, 6, and 8 without repetition, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Conditions**:
- We need to form a 5-digit number.
- The digits available are 0, 2, 4, 6, and 8.
- The number must be greater than 10,000, which means the first digit cannot be 0.

2. **Choose the First Digit**:
- The first digit can be chosen from the set {2, 4, 6, 8}.
- There are 4 options for the first digit (2, 4, 6, or 8).

3. **Choose the Remaining Digits**:
- After selecting the first digit, we have 4 digits left (including 0) from which we need to select the remaining 4 digits.
- The second digit can be any of the remaining 4 digits.
- The third digit can be any of the remaining 3 digits.
- The fourth digit can be any of the remaining 2 digits.
- The fifth digit will be the last remaining digit.

4. **Calculate the Total Combinations**:
- The total number of ways to arrange these digits can be calculated as follows:
- First digit: 4 choices (2, 4, 6, 8)
- Second digit: 4 choices (any of the remaining digits)
- Third digit: 3 choices (any of the remaining digits)
- Fourth digit: 2 choices (any of the remaining digits)
- Fifth digit: 1 choice (the last remaining digit)
- Therefore, the total number of combinations is:
\[ \text{Total Combinations} = 4 \times 4 \times 3 \times 2 \times 1 \]

5. **Perform the Calculation**:
- Calculate:
\[ 4 \times 4 = 16 \]
\[ 16 \times 3 = 48 \]
\[ 48 \times 2 = 96 \]
- Thus, the total number of 5-digit numbers that can be formed is **96**.

### Final Answer:
The total number of numbers that can be formed using the digits 0, 2, 4, 6, and 8 that are greater than 10,000, without repetition of digits, is **96**.