Let suppose that I have a box with $k$ different balls, each one with a different color.
At each time I have to extract a ball and observe the color. Then I put the ball back in the box.
How many extraction I need in order to see all the colors with probability at least $1-\alpha$?
This looks like a multinomial distribution, but instead of finding the probability of a certain result, I have to find the number of trials.