Given a bag of N balls numbered 1 to N. I'd like to calculate the expected (average?) number of draws needed to have probability P of drawing each of the N balls with replacement. For example, how many balls would I need to draw (with replacement) to have a 90% chance of drawing every ball? I believe the odds involve one or more infinite series, but my stat skills are way too rusty to be able to work it out. Thanks for any help.