Question

Randomness and discrete math:
I want to generate:
A set of random natural numbers S
where:
each element is between the natural numbers L and U
the cardinality of the set is a known constant C
and /the sum of the set is equal to a known constant P/ (at least with a probability of 9/10 or so)

What would L and U be given C and P?

I'm not looking for an answer just what I should call it/ where I should look/ how I can unpack the last requirement.

Thanks in advance.

Answer 1

One solution is to set L=1 and U=P/C but that has a huge amount of variation.