UnfixedArrangements | Topcoder Archive

Problem Statement

There are k slots numbered 1 through k, and you must assign a distinct integer between 1 and n, inclusive, to each slot. The resulting configuration is called an arrangement of k from n. An example of an arrangement of 3 from 5 is (2, 4, 3).

An arrangement is called unfixed if no integer is equal to the number of its slot. For example, the arrangement (2, 4, 3) is not unfixed because the integer 3 is in slot number 3. The arrangement (2, 4, 5), on the other hand, is unfixed.

Given ints n and k, return the number of unfixed arrangements of k from n.

Definition

Class:: UnfixedArrangements
Method:: count
Parameters:: int, int
Returns:: long
Method signature:: long count(int n, int k)
(be sure your method is public)

Constraints

n will be betwen 1 and 20, inclusive.
k will be between 1 and n, inclusive.

Examples

```
3
```
```
2
```
```
Returns: 3
```
The unfixed arrangements of 2 from 3 are (2,1), (2,3) and (3,1).
```
1
```
```
1
```
```
Returns: 0
```
The only arrangement of 1 from 1 is not unfixed.
```
2
```
```
2
```
```
Returns: 1
```
The arrangement (2,1) is unfixed.
```
5
```
```
3
```
```
Returns: 32
```

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