Lets say with have a game with 10 targets. In each turn the participant shoots X number of different and random targets, where X is a random whole number between 0 and 10 (included). Game ends when all targets were shot atleast once.
My question is: would the average amount of turns it takes to complete such game would change if the participant shoots exactly 5 (the everage of X) targets every turn? Why?
Clarification: Targets can be shot more than once.