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Probability of rolling all 6 dice faces

The probability of rolling every number from 1 to 6 with $N$ six-sided dice.
## Input
- A positive integer $N$.
- Your code must work for inputs up to and including 10, but may crash, error, or give incorrect output for larger inputs.
## Output
- A probability, $0 \le p \le 1$
- This is the probability of seeing every number from 1 to 6 at least once after rolling $N$ six-sided dice simultaneously.
- For inputs up to and including 10, your output is valid if rounding it to 6 decimal places results in the output shown in the test cases.
*Note that this means that if you find an incorrect algorithm that happens to give the correct first 6 decimal places for inputs from 1 to 10, that is still a valid entry.*
## Test cases
- Test cases are in the format `input : output`.
```text
1 : 0
2 : 0
3 : 0
4 : 0
5 : 0
~~6 : 0.0154320987654~~
~~TODO: test cases up to 10 to 6 decimal places~~
```
## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.
> Explanations are optional, but I'm more likely to upvote answers that have one.
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

The probability of rolling every number from 1 to 6 with $N$ six-sided dice.
## Input
- A positive integer $N$.
- Your code must work for inputs up to and including 10, but may crash, error, or give incorrect output for larger inputs.
## Output
- A probability, $0 \le p \le 1$
- This is the probability of seeing every number from 1 to 6 at least once after rolling $N$ six-sided dice simultaneously.
- For inputs up to and including 10, your output is valid if rounding it to 6 decimal places results in the output shown in the test cases.
*Note that this means that if you find an incorrect algorithm that happens to give the correct first 6 decimal places for inputs from 1 to 10, that is still a valid entry.*
## Test cases
- Test cases are in the format `input : output`.
```text
1 : 0
2 : 0
3 : 0
4 : 0
5 : 0
6 : 0.0154321
7 : 0.0540123
8 : 0.114026
9 : 0.189043
TODO: test case for 10 to 6 decimal places
```
## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.
> Explanations are optional, but I'm more likely to upvote answers that have one.
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

code-golf math dice