Answer to Question #31118 in Statistics and Probability for zoran

Question

Lets assume we have an urn with 20,000 numbers (1-20,000). Lets have 40 drawings of 20 numbers when after each drawing numbers are recorded and returned to urn.
How do I calculate the probability that no number will be drawn twice, 1 number will be drawn twice, 2 numbers will be drawn twice etc.
In other words what is the probability for a number to be drawn twice under such circumstances?

Thank you in advance for your help
zoran