If m numer of integers greater than 7000 can be formed with the digits 3, 5, 7, 8 and 9, such that no digit is being repeated, then the value of `(m)/(100)` is

Answer

To solve the problem of finding how many integers greater than 7000 can be formed using the digits 3, 5, 7, 8, and 9 without repetition, we can break it down into steps.

### Step 1: Identify the possible leading digits
Since we need to form numbers greater than 7000, the leading digit must be either 7, 8, or 9. This gives us three cases to consider.

### Step 2: Case 1 - Leading digit is 7
If the leading digit is 7, we can use the remaining digits 3, 5, 8, and 9 to form the rest of the number. We need to form a 4-digit number.

- **Remaining digits**: 3, 5, 8, 9 (4 digits)
- **Ways to arrange**: We can choose any 3 of the remaining 4 digits to fill the next three places.

The number of arrangements of 3 digits from 4 is given by:
\[ P(4, 3) = 4! / (4-3)! = 4! / 1! = 24 \]

### Step 3: Case 2 - Leading digit is 8
If the leading digit is 8, we can use the remaining digits 3, 5, 7, and 9.

- **Remaining digits**: 3, 5, 7, 9 (4 digits)
- **Ways to arrange**: Again, we can choose any 3 of the remaining 4 digits.

The number of arrangements is the same as in Case 1:
\[ P(4, 3) = 24 \]

### Step 4: Case 3 - Leading digit is 9
If the leading digit is 9, we can use the remaining digits 3, 5, 7, and 8.

- **Remaining digits**: 3, 5, 7, 8 (4 digits)
- **Ways to arrange**: We can choose any 3 of the remaining 4 digits.

The number of arrangements is again:
\[ P(4, 3) = 24 \]

### Step 5: Total arrangements
Now, we can sum up the arrangements from all three cases:
\[ \text{Total} = 24 + 24 + 24 = 72 \]

### Step 6: 5-digit numbers
Next, we consider 5-digit numbers. Since any 5-digit number formed from these digits will be greater than 7000 (as the smallest 5-digit number is 70000), we can use all 5 digits.

- **Ways to arrange**: The number of arrangements of all 5 digits is:
\[ 5! = 120 \]

### Step 7: Total count of valid numbers
Now, we combine the counts from the 4-digit and 5-digit cases:
\[ m = 72 + 120 = 192 \]

### Step 8: Calculate \( \frac{m}{100} \)
Finally, we need to find \( \frac{m}{100} \):
\[ \frac{m}{100} = \frac{192}{100} = 1.92 \]

### Conclusion
Thus, the value of \( \frac{m}{100} \) is **1.92**.