# Probability of unbalanced distribution of number of K elements in n sets

I have n sets and k elements with k>n. Each elements has the same probability (1/n) to be inserted in a set. All the elements have to be inserted in one single set.

I need to calculate the probability the difference of number of elements between the fuller set and the emptier one is at least X%.

For example, given 10 sets and 100 elements I need to calculate the probability one sets has at least the 10% of elements more than another.

-
OK, this is what you need. And what did you try to do that? –  Did Aug 3 '12 at 10:55
I thought in the beginning find all the possible combination of n number which the sum of all of them is equal to k. After that I should to enumerate all the sequence where min{Sn}/max{Sn}>=0.9. After that it's easy. But my mathematics lacks and I don't know how to go further.. I can solve it only by computational brute force but it is not good for my analytical purpose. –  cesare Aug 3 '12 at 12:05