A carnival game is set up so that a ball put into play has an equal chance of landing in any of 60 different slots. The operator of the game allows you to choose any number of balls and put them all into play at once. If every ball lands in a separate slot, you receive $1 for each ball played; otherwise, you win nothing. How many balls should you choose to play in order to maximize your expected winnings?
I believe that the equation for the expected winnings = (balls played)*(1-P(2 or more balls in same urn)). Since everything else is relatively straightforward, I want to find this P(2 or more balls in same urn). Is there a certain way of finding this? Or even better, is there a general form to find this probability given n balls and m urns?