Average # of trials to achieve success across multiple variables with different probabilities.

Question

Imagine you are rolling multiple sided dice. You start by rolling let's say 4 dice at a time with side numbers 6,7,8, and 9. What is the average number of attempts until all 4 dice have rolled a 1? (Upon success the die is removed). I've taken a basic high school stats course but I'm a little fuzzy on that and couldn't think of how to do this. (This is not what I want to calculate but I would prefer a general example being solved rather than bombard you with the specific variables actually at play)