Quote:
Originally Posted by Ether
If a fair die is thrown 420 times, what's the probability of getting exactly 70 of each number (1 thru 6)?
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Alright, not looking at any of the posts yet, this question looks like it's essentially "how many ways can you arrange 70 each of 6 options"
The formula for permutations with repetition is
Code:
n!/(n1! * n2! * ... * ni!)
So we have
Code:
n!/(n1! * n2! * ... * n6!) = (420!)/(70!)^6
So that's the total number of ways to get 70 exactly of 1 to 6.
To find the probability, divide by total number of ways to throw the dice, which is 6^420 since there are 6 options on each of 420 steps.
I get 5.99605*10^-7
In conclusion, not likely to happen
Edit: looks like I came a bit late to this thread
But it also looks like other people got the same thing. I guess this is correct then.