The largest 5-digit number having three different digits is

Options

A. 98978
B. 99897
C. 99987
D. 98799

Answer

To find the largest 5-digit number that has three different digits, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Largest Digit**:
The largest digit in the decimal system is 9. Since we want the largest 5-digit number, we will start with 9.

**Hint**: Always start with the largest digit available to maximize the number.

2. **Use the Largest Digit Multiple Times**:
Since we can use three different digits and we need to fill five places, we can use the largest digit (9) three times. This gives us "999" as the beginning of our number.

**Hint**: Repeating the largest digit helps in maximizing the value of the number.

3. **Choose the Next Largest Digits**:
After using 9 three times, we need to fill the remaining two places with the next largest digits. The next largest digit after 9 is 8, and then 7.

**Hint**: Always choose the next largest available digits to maintain the maximum value.

4. **Construct the Number**:
We can arrange the digits as follows:
- Use 9 three times: 999
- Use 8 and 7 for the remaining two places: 8 and 7.

The largest arrangement of these digits is 99,987.

**Hint**: Arranging the digits in descending order gives the largest possible number.

5. **Verify Against Options**:
Now, we can check the options provided:
- Option 1: 98,978
- Option 2: 99,897
- Option 3: 99,987
- Option 4: 98,799

The number 99,987 matches our constructed number.

**Hint**: Always double-check your answer against the provided options to ensure accuracy.

### Final Answer:
The largest 5-digit number having three different digits is **99,987**.