Probability of rolling all 6 dice faces [FINALIZED]
Now posted: Probability of rolling all 6 dice faces
The probability of rolling every number from 1 to 6 with $N$ six-sided dice.
- 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.
- 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 result when rounded to 6 decimal places for inputs from 1 to 10, that is still a valid entry.
- Test cases are in the format
input : output.
1 : 0 2 : 0 3 : 0 4 : 0 5 : 0 6 : 0.015432 7 : 0.054012 8 : 0.114026 9 : 0.189043 10 : 0.271812
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.