I would like to have the probability that some N samples of equiprobable events in M have no case that M has individual results that have more than one maximum value.
The code I am using in Mathematica 11 is:
Probability[Max[Array[x, bins]]<= max, Array[x, bins] [Distributed]
Multinomial distribution[balls, ConstantArray[1/bins, bins]]]
But, this becomes very slow with the cases that interest me. For example:
{balls, containers, max} = {100, 10, 20}
It has been running for several minutes on my Intel 4-core laptop reasonably fast.
Can performance be improved in any way to ensure that cases like this or a similar magnitude of values end up in less time?
