Maybe I have not explained my problem clearly,
There are 5000 persons, 1500 balls.
The ball is labeled with seriate number from 1 to 1500. And everyone selects 20 numbers randomly (not picking up balls but recording each number)
What's the propobility that a ball with number X (X is a number between [1,1500]) will be selected by N persons? (N<=5000)
I think the last part of ebaines's answer N!/(5000-N)! should be modified as
If I am wrong, please help to correct , many thanks.