Average number of rolls of die to see each side at least once

Question

Possible Duplicate:
A Question About Dice

You have a weighted n-sided die. Every side of the die is weighted differently where side n1 has a weight of w1, n2 has a weight of w2, ...

Estimate the average number of rolls needed to see every face at least once.

Answer 1

This is a variant of the coupon collector's problem

Formula (14a) is what you need.

Updated after comments.