Say I have a list of $n$ objects and I randomly choose one item from the list, but did not remove it. What is the method for calculating the probability I have chosen $x$ different items in the list after $n$ attempts?
For example, I am randomly choosing a number between $1$ and $100$. After how many attempts will I have had a $90\%$ chance that I chose $10$ distinct numbers?
Is there a specific name for this type of probability?