Probability: number of picks needed to be 99% likely to get one of each?

This comes from a problem in sampling a large, complex mixture. I have a large population (much more than 10^9 so effectively picking with replacement) and each member of this population is one of 1500 varieties. I want to sample this population to be sure that every variety is represented in this population. ... show more This comes from a problem in sampling a large, complex mixture. I have a large population (much more than 10^9 so effectively picking with replacement) and each member of this population is one of 1500 varieties. I want to sample this population to be sure that every variety is represented in this population. How many do I need to sample to be 99% confident that my mixture is complete?

Or, in another way

There are 1500 boxes. How many balls do I need to throw to reach 99% likelihood that every box will have at least one ball in it?

A general formula would be most appreciated.
Thanks.
3 answers 3