------
## 最终结论
```python
def permutation_coefficient(n, k):
    def factorial(x):
        if x == 0 or x == 1:
            return 1
        else:
            return x * factorial(x - 1)

    return factorial(n) // factorial(n - k)

# Test cases
assert permutation_coefficient(10, 2) == 90
assert permutation_coefficient(10, 3) == 720
assert permutation_coefficient(10, 1) == 10
```