We have $n$, 6-face fair dice. At each time $n$ dice are thrown independently. I want to calculate the probability of number of times we should throw dices before having at least one 6 from each of the dice.
We know that for one die to have one 6, the probability of $k$ failures obeys a Geometric Distribution with $p=1/6$ and expectation of 6.
How should I extend this to $n$ dices?