number of ways in which eight digit number can be formed using the digits from 1 to 9 without repetition, if first four places of the numbers are in increasing order and last 4 places are in decreasing order , is 'n' then `n/70` is equal to.

Answer

To solve the problem of forming an eight-digit number using the digits from 1 to 9 without repetition, where the first four digits are in increasing order and the last four digits are in decreasing order, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Selection of Digits**:
We need to select 4 digits from the available 9 digits (1 to 9) for the first half of the number, which will be in increasing order. The remaining 5 digits will then be used for the last half of the number, which will be in decreasing order.

2. **Choosing the First Four Digits**:
The number of ways to choose 4 digits from 9 is given by the combination formula:
\[ \binom{9}{4} \]
This represents the number of ways to select 4 digits from 9.

3. **Choosing the Last Four Digits**:
After selecting the first 4 digits, we have 5 digits left. We need to choose 4 digits from these remaining 5 for the last half of the number. The number of ways to do this is:
\[ \binom{5}{4} \]
Since we are choosing 4 out of 5, this is equivalent to simply selecting the one digit that will not be included.

4. **Calculating the Total Combinations**:
The total number of ways to form the eight-digit number is the product of the combinations calculated in steps 2 and 3:
\[ n = \binom{9}{4} \times \binom{5}{4} \]

5. **Calculating the Combinations**:
- Calculate \(\binom{9}{4}\):
\[ \binom{9}{4} = \frac{9!}{4!(9-4)!} = \frac{9 \times 8 \times 7 \times 6}{4 \times 3 \times 2 \times 1} = 126 \]
- Calculate \(\binom{5}{4}\):
\[ \binom{5}{4} = 5 \]

6. **Final Calculation of \(n\)**:
Now, substituting the values back into the equation for \(n\):
\[ n = 126 \times 5 = 630 \]

7. **Finding \(n/70\)**:
Finally, we need to calculate \(n/70\):
\[ \frac{n}{70} = \frac{630}{70} = 9 \]

### Final Answer:
Thus, the value of \(n/70\) is **9**.