Problem on Balls and Urns

I'm stumped on the following problem: I have m balls which I toss - at random - into k urns. Now, I remove the h urns that contain the smallest number of balls. How can I assess the probability that the number of balls remaining in the k-h urns left over is bigger than c*m (with 0 < c < 1) ?

Is there anybody here who can point out how to approach this type of problem?

Any help would be much appreciated!
- Ulf
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